Oxygen in Silicon, Volume 42 (Semiconductors and Semimetals)

Oxygen in Silicon SEMICONDUCTORS A N D SEMIMETALS Volume 42

a Semiconductors and Semimetals A Treatise

Edited by R . K . Willardson

Eicke R. Weber CONSULTING PHYSICIST DEPARTMENT OF MATERIALS SCIENCE SPOKANE, WASHINGTONAND MINERAL ENGINEERING OF CALIFORNIA AT UNIVERSITY Albert C. Beer BERKELEY CONSULTING PHYSICIST COLUMBUS. OHIO

Oxygen in Silicon SEMICONDUCTORS AND SEMIMETALS

Volume 42 Volume Editor

FUMIO SHIMURA SHILLIOKA INS717UTE OF S C l t N ( I A N I ) I F CHNOLOCY SHLILIOKA JAPAN

W ACADEMIC P R E S S , I N C . Hrrrc o u r i Bruce B; Compurri , Puh/r\Irc,r \

Boston

London

Sun Dicgo N P M 'Y o t h Sydney T d q o Torotito

This book is printed on acid-free paper @ COPYRIGHT 0 1994 BY ACADEMIC PRESS,INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY A N Y MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR A N Y INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION I N WRITING FROM THE PUBLISHER.

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LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Semiconductors and semimeta1s.-Vol.

1-New

York: Academic Press, 1966-

v.: ill.; 24 cm. Irregular. Each vol. has also a distinctive title. Edited by R. K. Willardson, Albert C. Beer, and Eicke R. Weber ISSN 0080-8784 = Semiconductors and semimetals

I . Semiconductors-Collected works. 2. Semimetals-Collected works. I. Willardson, Robert K. 11. Beer, Albert C. 111. Weber, Eicke R. QC6 l0.9.S48 621.3815'2-dc I9 85-6423 19 AACR2 MARC-S Library of Congress ISBN 0-12-752142-9 (v. 42)

[8709]

International Standard Book Number: 0-12-752142-9

Printed in the United States of America 94959697 9 8 7 6 5 4 3 2 1

Contents ...

LISTOF CONTRIBUTORS , PREFACE ,

Xlll

xv

Chapter 1 Introduction to Oxygen in Silicon F . Sh irn i i r ~

Chapter 2

The Incorporation of Oxygen into Silicon Crystals

W . Lit1 I . Introduction . 11. Silicon Crystal Growth I . Float Zone Silicon Growth 2. Crochralski Silicon Growth 111. Characteristics of Czochralski Silicon Growth , I. Dopant Distribution 2. “Unintended Dopants” 3. Effective Segregation Coefficient . 4 . Convection Flows in Crochralski Melt . 5 . Macroscopic Radial Impurity Uniformity , 6. Microscopic Inhomogeneity in Czochralski Silicon . I V . Oxygen Incorporation and Segregation in Czochralski Silicon Growth I . Incorporation Mechanism , 2 . Oxygen Segregation and Microscopic Inhomogeneity . V . Controlled Oxygen Silicon Growth . I . Normal Crochralski Growth , . 2. Magnetic Field Applied Crochralski Growth (MCZ) . , 3. Continuous Czochralski Silicon Growth . . V l . Summary . References .

Chapter 3

9 10 10

12 15 IS 16 19

20 21 22 24 24 34 37 31 42 46 50 50

Characterization Techniques for Oxygen in Silicon

T. J . Shqffrirr and D . K. Schrodrr 1. Introduction . 11. Physical Techniques . . I . lnfrared Spectroscopy

53 55 55 V

vi

CONTENTS

2. Transmission Electron Microscopy 3. X-Ray Diffraction and Topography 4. Secondary Ion Mass Spectrometry . Ill. Chemical Techniques . 1. Defect Etches . 2. Inert Gas Fusion . . 3. Activation Analysis Techniques . IV. Electrical Techniques . 1. Deep Level Transient Spectroscopy 2. Recombination Lifetime . 3. Generation Lifetime . V. Summary . References .

.

.

58 62 66 69 69 12

t

.

74 77 78 79 81 85 86

Chapter 4 Oxygen Concentration Measurement

W . M . Bullis I. Introduction

.

11. Infrared Absorption Measurements Under Ideal Conditions

.

Ill. Infrared Spectrometers . . I . Dispersive Infrared Spectrometers . 2. Fourier-Transform-Infrared Spectrometers . IV. Analysis of Oxygen Spectra . I . Baseline . 2. Analysis Method: Peak Height or Integrated Area? . . 3. Multiple Reflection and Interference Fringes . 4. Spectrum Collection Method: Air Reference or Difference? 5 . Reference Specimen Characteristics . 6. Back-Surface Condition . 7. Free-Carrier Absorption . 8. Interference from Absorption Peaks Due to Precipitates . 9. Specimen Temperature . . . . V. Absolute Determinations and Calibration Factors . . I . Calibration Factors for Room Temperature Measurements 2. Routine Absolute Measurements in Heavily Doped Silicon VI. Standards and Reference Materials . I . Standard Test Methods 2. Certified Reference Materials . VII. Summary . Acknowledgments . References .

95 99 102 102

107 I I3 113 I 15 118 121 121 122 128 134

135 136 136 142 144 144 14.5 147

147 148

Chapter 5 Intrinsic Point Defects in Silicon S . M . Hu 1. Introduction . 11. Swirl Defect Manifestation of Intrinsic Point Defects

153 156

vii

CONIENTS

111. Thermal Defects in Silicon . I V . Self-Diffusion . . I . Point Defects and Self-l)ilfusion 2 . Self-Diffusion from Isotope Experiments . 3 . Self-Diffusion from Kinetics of Extended Defects . V . Coexistence of Vacancies and Self-lnterstitials in Silicon . V I . Interstitial Configuration and Charge-Enhanced Migration , I . Geometrical Configurations and Migration Pathways of the Self-Interstitial . 2. Charge-Enhanced and Athernial Migration of the Self-Interstitial VII. Formation and Migration Parameters of Point Defects . , I . Studies of Point Defects from Irradiations . 2 . Vacancy Formation Energy from Positron-Lifetime Measurements 3 . Point Defect Concentrations rrom Thermal Expansion Measurements 4. Estimation of Self-lnterstitial Concentration from Oxygen Precipitation . 5 . Diffusivity of the Self-lnter,titial from Membrane Experiments . 6. Defect Parameters from Model-Fitting Au and Pt Diffusion . VIII. Defect Energetics and Pathways from Theoretical Calculations . 1X. Summary . Reference5 ,

i59 160

160 161 162 164 166 166 170 172 172 175 175 176 177

178 179 184 185

Chapter 6 Some Atomic Configurations of Oxygen

B . Pqjot I . Introduction

.

11. Spectroscopy of Localized Mode5 in Semiconductors 1. Localized Modes and Resonant Modes .

Ill.

IV.

V.

V1.

VII.

2. lntensities . 3 . Stress-Induced Effects Interstitial Oxygen . I . Static Properties . . 2. Dynamic Properties 3 . Perturbation by Foreign Atoms . Quasi-Substitutional Oxygen . 1 . Spectroscopies o f the Oxygen-Vacancy Defect 2. Thermal Stability . . 3 . Other 0-Related Irradiation Defects . Comparison with Other Light Element Impurities 1. Carbon . 2 . Nitrogen . 3 . Hydrogen . . Oxygen in Other Semiconductors I . Germanium . . 2 . Gallium Arsenide . . Summary . Acknowledgments . References .

191 194 194 196

.

1%

. .

. .

.

. .

. . .

. . .

200 200 210 21 I 217 217 220 222 224 224 226 228 233 233 236 243 244 245

viii

CONTENTS

Chapter 7 Electrical Properties of Oxygen in Silicon J . Michel and L . C . Kimerling I. Introduction

. . . . . .

.

11. Thermal Donors . 1. Donor Introduction

.

2. Spectroscopy . 3. Heat Treatment at 350-500°C . 4. Atomic and Electronic Structure . 5 . Current Understanding and Unresolved Issues 111. New Donors . References .

.

.

. . .

251 251 252 254 266 211 280 282 284

Chapter 8 Diffusion of Oxygen in Silicon

R . C . Newman and R . Jones I. Introduction

.

11. Direct Measurements of Normal Oxygen Diffusion

.

. 1 . Single Oxygen Diffusion Jumps . . . 2. Profiles 3. Summary . . 111. Indirect Measurements of Normal Oxygen Diffusion I . Do,,Determined from Oxygen Precipitation at High Temperatures 2. Oxygen Aggregation at Intermediate Temperatures . 3. Oxygen Aggregation at Low Temperatures . 1V. Enhanced Oxygen Diffusion Not Involving Hydrogen . I . Effects Due to the Injection of Vacancies and I-Atoms by 2 MeV Electron Irradiation . . 2. The Effects of Excess /-Atoms 3. Rapid Diffusion of Di-Oxygen Defects . 4. Effects Due to Carbon . . 5. Effects Due to Metallic Contamination . 6. Summary . V. Silicon Containing Hydrogen Impurities . 1. Silicon Heated in Hydrogen Gas . 2. Silicon Heated in RF Plasma . 3. An Outline Model and Summary . VI. Theoretical Modeling of Oxygen Diffusion . 1 . Theoretical Methods . 2. Theory of the Diffusion Constant . 3. Interstitial Oxygen . 4. Diffusion of 0, Catalyzed by Hydrogen . . 5. The Oxygen Dimer . 6. Other Oxygen Aggregates . . V11. Constraints on Models of Thermal Donor Centers V111. Summary . Acknowledgments . . . References . . .

. . . . . . .

. . . . . . . . . .

. .

.

. .

.

. . . .

290 292 293 296 298 298 299 303 305 308 309 312 314 316 317 317 318 319 323 324 326 327 331 332 335 339 341 342 345 341 347

ix

CON1 ENTS

Chapter 9 Mechanisms of Oxygen Precipitation: Some Quantitative Aspects

T . Y . Tan und W . J .

7'ciyIor

I . Introduction . 11. Volume Shortage Associated with Oxygen Precipitation 111. Precipitate Nucleation I . The Homogeneous Nucleation Model , 2. The Strain Relief Models IV. Precipitate Growth . I. The 0, Diffusion-Limited Precipitate Growth Behavior 2. The Dominant Strain Relief Mechanism: I-Emission . V . The Effect of Carbon V1. Defect Generation . 1. Si Self-Interstitial Gener-ation , 2 . Prismatic Dislocation Loop Punching . V I I . Summary: The Free Energy and Flux Balance Treatment of Precipitation Problem References .

.

. .

353 357 358 359 362 367 367 37 I 374 379 379 379

the Oxygen 386 387

Chapter I0 Simulation of Oxygen Precipitation

M . Schrrms I. Introduction . 11. Model Types . I . Nucleation Models 2. Deterministic Growth Models , 3. Combined Nucleation and Growth Models . 4. Monte Carlo Models , 5. Models Based on Rate 01' Fokker-Planck Equations 111. Models and Experimental Rewlfs . I . General Kemarks . 2. One-, Two-. and Three-Step Thermal Cycles . 3. Multistep Thermal Cycle\ 1V. Computer-Aided Design of Oxygen Precipitation , . I . Substitutional Annealinga 2. Influence of Process Variations . V . On the Interactions of Oxygen with Other Defects . 1. Current Models . 2. Generalized Precipitation i-:quations . V I . Summary . References .

Chapter I 1

39 I 393 393 396 400 402 404 413 413 416 424 47-8 42X 43 I 435 435 441

443 444

Oxygen Effect on Mechanical Properties

K . Sutnino and I . Yonrnupi I Introduction 11 Plastic Deformation and DisloLatlon\

in

Silicon Crystals

450 45 I

X

CONTENTS

111. Influence of Dispersed Oxygen Atoms on the Mobility of Dislocations

in Silicon . . . 1. Methodological Problems in the Measurement of Dislocation Velocities . 2. Velocity of Dislocations in High-Purity Silicon . 3 , Velocity of Dislocations in Silicon Containing Oxygen Impurities 4. Morphology of Dislocations in Motion . 5. Interpretation of the Oxygen Effect on Dislocation Velocity . IV. Immobilization of Dislocations by Oxygen . . . 1. Release Stress of Dislocations Immobilized by Oxygen Impurities 2. State of Oxygen Segregated on Dislocations . . . V . Effect of Oxygen on Dislocation Generation . I , Generation of Dislocations . 2. Oxygen Effect on Dislocation Generation . . V1. Mechanical Properties of Silicon as Influenced by Oxygen Impurities . 1 . Mechanical Properties of High-Purity Silicon Crystals 2. Oxygen Effect on Mechanical Properties of Dislocation-Free Crystals . 3 . Oxygen Effect on Mechanical Properties of Dislocated Crystals 4 . Theoretical Derivation of Yield Characteristics . . 5. Wafer Strengthening by Oxygen Impurities . VII. Influence of Oxygen Precipitation on Mechanical Strength 1. General Features in the Softening of Silicon Related to Precipitation of Oxygen . . 2. Yield Strength of CZ-Si with Oxygen Precipitation . . 3. Mechanism of Precipitation Softening V111. Effects of Nitrogen and Carbon Impurities on Mechanical Properties of Silicon . 1. Nitrogen Effect . 2. Carbon Effect . . . 1X. Summary . References .

454 454 455 451 460 46 1 463 463 461 469 469 472 474 414 476 471 48 I 488 490 490 493 496 499 499 504 504 5 10

Chapter I2 Grown-in and Process-Induced Effects W . Bergholz 1. Introduction . . . 11. Oxygen Precipitation During High-Temperature Processes . . I . Overview: Morphology and Phases of Oxygen Precipitates 2. Factors That Determine the Type of Oxygen Precipitate . 3. Oxygen Precipitation in Different Temperature Regimes . 4 . Multiple-Step Temperature Annealings . 5. Other Factors That Affect Oxygen Precipitation . . 6. Oxygen-Related Defects and Process-Induced Defects Ill. Grown-in Defects: Precipitation and Intrinsic Defect Aggregation During Crystal Growth . 1. Oxygen Precipitation During Crystal Growth . . . 2 . Intrinsic Defects . 3. Grown-in Defects and Gate Oxide Quality .

513 515 515 522 526 540 544 547 55 I 55 1 552 564

xi

C‘ONTFNTS

4. Speculations on the Origin-Formation Mechanisms of Grown-in . Defects I V . Summary . References .

570 57 I 572

Chapter 13 Intrinsic/lnternal Gettering

F. Shimura 1. lntroduction . 11. Surface and Interior Microdefect\

.

I . Surface Microdefects

2. Interior Microdefects 3. Summary of Process-Induced Microdefects

.

517 579 580 583 590 593 593 596 596 599 599 599 606 610 610 611 612

.

614

.

615

. .

619 621 622 623 62.5 625 628 630 633 634 63.5 636 640 647 651

.

. .

I l l . Gettering . I . General Remarks . 2. Elimination of a Contamination Source . 3. Intrinsicilnternal Gettering IV. Oxygen Behavior in Silicon I . Oxygen Effect o n Silicon Wafer Properties . 2. Oxygen Precipitation and Redissolution , . 3 . Oxygen Out-Diffusion and Denuded Zone Formation V. Internal Gettering Process and Mechanism . , I . Thermal Cycle . 2. Gettering Mechanism 3. Gettering Sinks . VI. Summary . References .

. .

. .

. . .

Chapter 14 Oxygen Effect on Electronic Device Performance

H . T sity N I. Introduction . I I . Device Characteristics and (‘ry5tal Defects . . I , Device Structure vs. Cryrtalline Defects . . 2. Failure Modes in LSI Devices . Ill. Defect Generation . . I . Oxygen Precipitate Related Modes . 2. Residual Stress of SiOz Film . , 3. Oxygen Related Defects hy Ion Implantation . 4. Oxide Film Degradation 5 . Lattice Defect Generation h i e t o Heavy Metal Contamination . I V . Improvement of Device Yield I . Intrinsic Gettering Application to VLSl . . 2 . Homogenization of Precipitated Oxygen . . 3. Intrinsic Gettering Application of Epitaxial Wafers to VLSl . 4. Getterability for Heavy Metal Impurities .

. . . . . .

.

xii

CONTENTS

5 . Control of Mechanical Strength 6. Advanced Intrinsic Gettering V. Summary . Acknowledgments . References .

INDEX

.

CONTENTS OF PREVIOUS VOLUMES.

.

. .

t

.

. . . . .

652 660 663 663 664 665 680

List of Contributors Numbers in parenthe5es indicate the page\ on which the authors' contribution5 hegin

W. BERGHOLZ ( 5 13). Siemens A G , WernerM*erkstr.2 , 8400 Regensburg, Germuny. W . M . BULL.IS ( 9 3 , Mutrriuls d; Metrologv, 1477 Enderby Way, Sirnny 1~ I P , CUliforn iu 94087. S . M. H u , (153) IBM East Fishkill Fucdity, 1580 Route 52, HopeM'ell Jct., N r w York 12533. R . JONES (290). Depurtrnent of P1iy.sic.s. University of Exeter, Stocker Roud, E.\-etc.r EX4 4 Q L . U K . L . C . KIMERLING (25 l ) , Deprrrttnent of Materiuls Science and Engineering. Mussuchusettt.s lnstitutr o f Technology, Rootn 13-5094, Carnhridge, Mussuchusi.tts 02139. W . LIN(9),AT&T Bell Luhorutories, 555 Union Blvd., Allentm-n, Pennsyltwiiu 18103. J . MICHEL(25I ) , Departtnrnt o f Muterials Science und Engitwering, Massachusetts Institutcl (?f Technology. Room 13-5094, Cambridge, Mirssuchrrsetts 02139. R . C . NEWMAN (290). Intet-tli.sc~iplinaryResearch Center, University of London, Prince Consort Roud. London S W7 2BZ, U K . B . PAJOT(1911, Groupr dri Physique des Solides, UnivrrsitP Paris 7 et Paris 6 , Tour 23, 2 p1uc.e J i r s s i e u . F-75251 Paris Cedex 05, Frunce. M. SCHREMS (391 ), Integrutc,d Circuir Advanced Process Engineering Depurtment, Toshiba Corporulion, Kornukai. Toshibu-rho, Saiwwiku, Kal-lwsaki 210, Japan. D. K . SCHRODER ( 5 3 ) . Centcr jiir Solid Stute Electronics Research, Arizonu Stute University, Ti.rnpe. Arizona 85287. T . J . SHAFFNER ( 5 3 ) , Texas Instriimrnts, Incorporated, Marerials Science Lahorutor.y, P.O. Box 6559.16, Dullus, Texas 75265. I;. SHIMURA (577),Department (fMaterials Science, Shizuoku Institute o f Science and Technology, 2200-2 T o y o . s a ~ wFukuroi, ~ Shizuoku 437, Japan. xiii

xiv

LIST OF CONTRIBUTORS

K. SUMINO (450), Institute for Materials Research, Tohoku University, Katahira, Sendai 980, Japan. T. Y . TAN(353), Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27706. W. J . TAYLOR (353),Motorola APRDL, Mail Stop K-10,3501 Ed Bluestein R d . , Austin, Texas 78721. H. TSUYA(619), Research and Development Group, NEC Corporation, Shimokuzawa, Sagamihara 229, Japan. I . YONENAGA (450), Institute for Materials Research, Tohoku University, Katahira, Sendai 980, Japan.

Preface Silicon, which has been and will be the dominant material in the semiconductor industry, will carry us into the ultra-large-scale integration (ULSI) era. The silicon semiconductor industry now requires the minimum concentration of harmful defects and impurities in silicon crystals in order to improve the device manufacturing yield and operation performance. These requirements are becoming increasingly stringent as the technology changes from LSI t o U L S I . At present almost all the silicon wafers used for microelectronic circuit fabrication are prepared by the Czochralski (CZ) method or its modification; these silicon wafers contain oxygen on the order of atoms/ cm'. N o matter how much oxygen is incorporated in silicon wafers. the resulting impurity critically affects the properties and yield of electronic devices because of the effect o n the mechanical and electrical properties of the wafers as well as on the lattice defects incorporated. Recently it has been recognized that t h e surface microroughness of polished silicon wafers. which can greatly affect t h e device performance, may also be related to the impurity and related microdefects. Under the circumstances, for the last three decades both academia and industry have devoted a great deal of attention to the investigation of the behavior of oxygen in silicon. The investigation was particularly extensive during the decade when the beneficial effect of oxygen on device performance was discovered. Even greater attention should be devoted to this subject as the technology of microelectronic circuits approaches ULSI and beyond. It is therefore extremely important to understand the behavior of oxygen in silicon from both the scientific and the engineering points of view and to control not only the oxygen concentration but also its agglomeration phenomenon. Accordingly, this volume reviews the latest understanding of the behavior and roles of oxygen in silicon from both the experimental and theoretical points of view. The fourteen chapters, written by recognized authorities representing industrial and academic institutions, cover thoroughly the phenomena related to oxygen in silicon from crystal growth to device fabrication processes. Some indispensable diagnostic techniques for oxygen are covered as well. Because the chapters may be read independently, the editor retained some overlapping among the chapters. xv

xvi

PREFACE

Moreover, all the related discussions among the chapters may not necessarily agree with each other. The editor intended to leave such argument to show that oxygen in silicon is still a highly debated subject. The authors of the individual chapters were encouraged to describe the fundamentals in order to make the volume as useful as possible both to graduate students and to scientists from other disciplines as well as to active participants in the exciting arena of silicon-based microelectronics research. The editor’s experience in working on semiconductor technology at an electronic device manufacturer, at an electronic materials manufacturer, and at a university should ensure that this volume is one in which both the fundamental and practical matters of this interdisciplinary area will be discussed. Finally, I trust that this volume will prove to be an important and timely contribution to the semiconductor and microelectronics literature. Fumio Shimura

SEMICONDUCTORS A N U SEMIMETALS. VOL. 42

CHAPTER 1

Introduction to Oxygen in Silicon F . Shimura DEPARTMENT OF MATERIALS SCIENCE SHIZUOKA INSTITUTE OF SCIENCE A N D TECHNOLOGY, SHIZUOKA. JAPAN

The growth of single crystals of silicon from high-purity polysilicon is a critical beginning step for the fabrication of electronic devices based on silicon. Although various techniques have been utilized to convert polysilicon into single crystals of silicon, two techniques have dominated the production of silicon single crystals because they meet the requirements of the microelectronic device technology. One is a zone-melting method commonly called the ,flour-zone (FZ) method (Keck and Golay, 1953; Keck et al., 1954),and the other is a pulling method generally called the Czochrulski (CZ) mc4iod although it should be called more properly the Ted-Little method (Teal and Little, 1950). It is estimated that about 80% of the single crystal silicon used for device manufacturing is produced by the pulling method (Zulehner and Huber, 19821, i.e., CZ silicon, and that is a reason we have a great interest in the crystals. In the Teal and Little method, which modified the technique to determine the crystallization velocity of metals developed by Czochralski (Czochralski, 1918). a single crystal is grown by pulling from the melt contained in a quartz or vitreous silica (SO,) crucible. The surface of crucible that contacts the silicon melt is gradually dissolved (Chaney and Varker, 1976) as a result of the reaction SiO,

+ Si+

2SiO.

(1)

This reaction enriches the silicon melt with oxygen. Most of oxygen atoms evaporate from the melt surface as volatile silicon monoxide ( S O ) , but some of them incorporate into a silicon crystal through the crystal-melt interface (Kaiser and Keck, 1957). These oxygen atoms can greatly affect the electrical, chemical, mechanical, and physical properties of a silicon crystal. In 1954 the presence of oxygen in silicon single crystals was first demonstrated with a phenomenon showing the large resistivity change induced by heat treatment (Fuller et al.. 1954), although the phenomenon was not correlated to oxygen in silicon at that time. Fuller et al. found 1 Copyright @ 1994 hy Academic P r e s . Inc.

All rights of reproduction In any form reserved ISBN &I?-752142-9

2

F. SHIMURA

that the resistivity of CZ silicon crystals changed greatly when the crystals were heat treated at 430-450°C. By heating the crystals to temperatures above about 500°C the change was reversed. This finding surely provided the momentum; since then oxygen in silicon has been one of the most important subjects in the field of silicon materials science and engineering. Two years later, by means of infrared absorption spectroscopy, Kaiser, Keek, and Lange first confirmed that CZ silicon single crystals contain oxygen as an impurity in concentrations on the order of magnitude higher than the usual doping impurities (Kaiser, Keck, and Lange, 1956). At the same time, the oxygen concentration was correlated to the intensity of the infrared absorption band at 9 pm or 1106 cm-' (Hrostowski and Kaiser, 1957; Kaiser et al., 1956; Kaiser and Keck, 1957), and shortly Hrostowski and Kaiser obtained the solubility of oxygen in silicon (Hrostowski and Kaiser, 1959). On the basis of the infrared absorption analysis, it has been established that oxygen atoms incorporated into silicon dominantly occupy interstitial sites in the silicon lattice with average positions midway between two neighboring silicon atoms along the four equivalent (1 1 1) bond directions (Kaiser et al., 1956).Two neighboring silicon atoms give up their covalent bond and engage with an interstitial oxygen atom instead, forming an isosceles triangle with Si, 0, Si at the corners. With Si-0 distances of 1.6 A and assuming the Si-Si distance to be essentially unchanged (2.34 the bond angle Si-0-Si is approximately 100". Because of the crystal symmetry, the nonlinear Si-0-Si bridge has six equivalent positions. Transition between those six positions occur frequently because the transition does not involve the breaking of chemical bond; that is, it requires a small activation energy (Corbett and Watkins, 1961). Soon after, the work by Fuller et al. (1954) on the resistivity change induced by heat treatment and Kaiser et al. (1956) on the verification of impurity oxygen in CZ silicon single crystals, it was confirmed that oxygen as an impurity incorporated into CZ silicon in an electrically neutral form can be caused to provide donors, called thermal donors, in the low-temperature range (400-500°C) and the states can be annihilated by a subsequent at higher temperatures (>650"C) (Fuller and Logan, 1957; Kaiser, 1957; Kaiser, Frisch, and Reiss, 1958). Recent investigation has shown, however, more complicated behavior of oxygen-related carriers, which greatly depends on the heat-treatment temperature (Capper, et al., 1977). Eventually, another type of oxygen donor, called new donor (Kanamori and Kanamori, 1979), can be formed in CZ silicon subjected to heat treatment in the temperature range between 600 and 1000°C. For convenience, the oxygen donors formed around 450°C are occasionally referred to as old donors. The new donors can be annihilated by heat

A),

1.

INTRODU("rI0N T O OXYGEN IN SILICON

3

treatment at a high temperature, e.g., >IIO0"C (Cazcarra and Zunino, 1980). Thus a standard heat treatment in the temperature range between 650 and 800°C for the annihilation of old donors can cause the generation of new donors. In order to avoid the generation of new donors during old donor annihilation, therefore, rapid thermal processing (RTP) at 650°C for a short time, on the order of seconds, has been suggested as an effective alternative donor-annihilation step (Wilson, Paulson, and Gregory, 1985). Since the concentration of oxygen incorporated into CZ silicon crystals exceeds the solid solubility in the practical temperature range, the supersaturated oxygen can precipitate during subsequent heat treatment. Patel and Chaudhuri (1962) showed that the yield point of a "dislocation-free" CZ silicon crystal is lowered by almost a factor of 5 after heat treatment at 1000°C for 76 hrs. The degradation in mechanical strength of silicon has been attributed to dislocations generated by the precipitation of supersaturated oxygen (Kondo, 1981 ; Patel, 1977; Patel and Chaudhuri, 1962; Sumino, 1981; Yasutake, Umeno, and Kawabe, 1980). This yield behavior in semiconductors has been shown to be governed by the dynamical behavior of dislocations (Patel and Chaudhuri, 1962) as first pointed out for LiF by Johnston and Gilman (Johnston and Gilman, 1959). It has been recognized that the oxygen precipitation can cause warpage of silicon wafers during thermal processing (Leroy and Plougonven. 1980; Shimizu, Watanabe, and Kakui, 1985). With regard to the characterization of lattice defects generated by oxygen precipitation in CZ silicon, there have been a large variety of observations by means of transmission electron microscopy (TEM) for the materials heat treated under various conditions (Bender, 1984; Bourret, Thibault-Desseaux, and Seidman, 1984; Gaworzewski et al., 1984; Maher, Staudinger, and Patel, 1976; Matsushita, 1982; Ponce, Yamashita, and Hahn, 1983; Shimura, Tsuya, and Kawamura, 1980a). The first and most thorough characterization was made by Maher et al. in 1976, and then followed by Shimura et al. in 1980. In brief, the defects produced by oxygen precipitation in CZ silicon are ( I ) SiO, precipitates ( X = 21, (2) extrinsic-type perfect dislocations associated with the precipitates, and (3) extrinsic-type stacking faults associated with the precipitates. That is, it may define that impurity oxygen atoms, SiO, precipitates, and dislocations or stacking faults are the first-, second-, and third-order defects in CZ silicon. The second- and third-order defects can degrade the mechanical strength of CZ silicon wafers. Because of the detrimental effect of oxygen, in terms of the electrical and mechanical properties. on silicon wafers, oxygen had been recognized as a harmful impurity in silicon for many years. Therefore, on the

4

F. SHIMURA

basis of the CZ method several new crystal growth techniques that minimize the incorporation of oxygen into silicon crystals were investigated (Hoshi, et al., 1980; Suzuki, et al., 1981; Watanabe, et al., 1981). One of them is the magnetic-field-applied CZ (MCZ) method, which utilizes the effect of magnetic field applied to the silicon melt on melt flow damping. Although at this moment the MCZ method has been used to grow silicon crystals with a wide variety of oxygen concentrations, from low to high, that cannot be obtained by the conventional CZ method (Ohwa, et al., 1986; Suzuki, et al., 1986; Takasu, et al., 1990), the technique was first applied by Hoshi, et al. (1980) to grow CZ silicon crystals that contain impurity oxygen of low concentration. The second epoch-making year might be 1976 when Rozgonyi, Deysher, and Pearce first reported that interior defects produced by oxygen precipitation can be effective to suppress epitaxial stacking faults or the origin in CZ silicon wafers. This phenomenon showing a beneficial effect of impurity oxygen in CZ silicon was first reported as in situ gettering (Rozgonyi, et al., 1976). In 1977, Tan, Gardner, and Tice further clarified this phenomenon and termed it intrinsic gettering, so as to distinguish it from extrinsic gettering, which had been commonly used in the silicon device industry. Since then, the intrinsic gettering or internal gettering (IG) technique has been extensively investigated and applied to the fabrication of microelectronic devices using CZ silicon wafers. Because the IG effectiveness depends on the type and density of interior defects, which in turn depend on the initial oxygen concentration of the silicon wafer, annealing temperature, and time, a great deal of attention has been devoted to the investigation on the behavior of oxygen in CZ silicon both in the silicon academia and industry. Although the growth process and the related phenomena of oxygen precipitates have been extensively investigated (Patel, 1981; Lin, 1990), the nucleation process has not been completely understood yet. Homogeneous nucleation is nucleation from a homogeneous phase, as it is called, in which nucleation occurs randomly; while, catalyzing nucleation, where discontinuities such as lattice defects and second-phase particles in the matrix supply the nucleation sites, is called heterogeneous nucleation. Heterogeneous nucleation requires far less energy than homogeneous nucleation and is by far the more commonly observed in any system. Based mainly on the analyses of experimental results, it has been proposed by different investigators that the nucleation for oxygen precipitation in silicon would be a homogeneous process (Freeland, et al., 1977; Osaka, Inoue, and Wada, 1980), a heterogeneous process (Ravi, 1974; Shimura, Tsuya, and Kawamura, 1980b), or a combination of homogeneous and heterogeneous processes (Batavin, 1970). The major difficulties in this

I.

INTRODLICTION TO OXYGEN I N SILICON

5

argument may partly lie in the definition of homogeneous and heferogen ~ w i i s(Hu. 19861, although the physical difference between them is very clear, and in uncertainty on whether the process experimentally observed is the nucleution or g r o w f h process of oxygen precipitates. Putting the definition aside, it has been widely accepted that oxygen precipitation depends greatly not only on the initial oxygen concentration, i.e.. the oxygen supersaturation ratio, but also on various heterogeneous fucfors (Shimura and Tsuya, 1982). For example, subsidiary impurities such as carbon (Kishino, Matsushita, and Kanamori, 1979: Kung, Forbes, and Peng. 1983; Oehelein, et al.. 1981; Shimura. 1986; Usami, Matsushita. and Ogino, 1984) and nitrogen (Chiou, et al., 1984; Shimura and Hockett, 1986). In particular. a significant enhancement effect of oxygen precipitation due to the presence of carbon atoms has been widely observed since Kishino et al. first reported the phenomenon in 1979. In addition. the effect of thermal history on oxygen precipitation has been strikingly shown for silicon samples obtained from various positions of a CZ silicon ingot grown by the continuous-feeding CZ method (Shimura, 1991). Moreover, in addition to the beneficial effect of oxygen in silicon in terms of the 1G capability. it has been recognized that CZ silicon containing more oxygen as an impurity is less vulnerable than oxygen-lean FZ silicon to thermal stress in the device fabrication processes (Leroy and Plougonven, 1980; Hu, 1977). High-temperature processing of silicon wafers during electronic device manufacturing often produces sufficient thermal stresses to generate slip dislocations and warpage (Leroy and Plougonven, 1980: Takasu, et al.. 1981). These effects bring about yield loss due to leaky junctions, dielectric defects, and reduced carrier lifetime, as well as reduced photolithographic yield because of the degradation of wafer flatness. Deformation experiments have systematically shown that FZ silicon is more easily deformed than CZ silicon before preheating, while after preheating CZ silicon becomes more susceptible to plastic deformation (Kondo, 1981). A very drastic difference in the mechanical strength has been observed between F% and CZ silicons when they contain dislocations; that is, CZ silicon is much stronger than FZ silicon against thermal stresses (Sumino, et al., 1980). The difference in mechanical strength is attributed to the difference in the concentration of oxygen and associated defects (Kondo. 1981; Sumino, et al.. 1980; Patel and Chaudhuri. 1962; Yonenaga, Sumino, and Hoshi. 1984). This difference in mechanical stability against thermal stress is the dominant reason why CZ silicon crystals have been used almost exclusively for the fabrication of 1Cs whose level of integration requires a large number of thermal process steps. Howevet, it should be noted that as mentioned previously oxygen, if it

6

F. SHIMURA

precipitates too much, in CZ silicon can degrade the mechanical strength of the wafer. In summary, no matter how much oxygen is incorporated in silicon wafers used for the fabrication of electronic devices, the impurity critically affects the properties and yield of the devices because of the following three factors: (1) internal defects produced by oxygen precipitation benefit the gettering effect (IG),(2) mechanical strength of silicon wafers greatly depends on the oxygen concentration and state, i.e., dissolved oxygen atoms or SiO, precipitates, and (3) oxygen donors are formed at a specific temperature. Consequently, it is very important to understand the behavior of oxygen from the electrical, chemical, and structural points of view, and to control not only the concentration but also the precipitation in silicon. All these issues will be discussed and reviewed in detail from the experimental and theoretical points of view in the following chapters of this volume. Finally, we would like to emphasize that oxygen in silicon is still, and will be further, one of the hottest subjects in the field of silicon-based materials science and technology.

REFERENCES Batavin, V . V. (1970). Sov. Phys. Crystuogr. 25, 100. Bender, H. (1984). Phys. Stat. Sol. ( a ) 86, 245. Bourret, A.. Thibault-Desseaux, J., and Seidman, D. N. (1984). J. Appl. Phys. 55, 825. Capper, P., Jones, A. W., Wallhouse, E. J., and Wilkes, J. G. (1977). J. Appl. Phys. 48, I 646. Cazcarra, V. and Zunino, P. (1980). J . Appl. Phys. 51, 4206. Chaney, R. E.. and Varker, C. J . (1976). J. Crystal Growth 33, 188. Chiou. H. D., Moody, J., Sandfort, R., and Shimura, F. (1984). In VLSI Science and Technologyll984, K. E. Bean and G. A. Rozgonyi, (eds.), p. 59. The Electrochemical Society, Princeton, N.J. Corbett, J . W., and Watkins, G . D. (1961). J. Phys. Chem. Solids 20, 319. Czochralski, J. (1918). 2. Phys. Chern. 92, 219. Freeland, P. E., Jackson, K. A., Lowe, C. W., and Patel, J. R. (1977). Appl. Phys. Lett. 30, 31. Fuller, C. S., Ditzenberger, J. A,, Hannay, N. B., and Buehler, E. (1954). Phys. Rev. 96, 833. Fuller, C . S . , and Logan, R. A. (1957). J. Appl. Phys. 28, 1427. Gaworzewski, P., Hild, E., Kirschit, F. G . , and Vecsern YCs, L. (1984). PhyA. Stat. Sol. ( I ) 85, 133. Hoshi, K.. Suzuki, T., Okubo, Y., and Isawa, N. (1980). Ext. Abstr., 157th Electrochem. SOC. M e e t . , p. 811. Hrostowski, H. J., and Kaiser, K. H. (1957). Phys. Rev. 107, 966. Hrostowski. H. J., and Kaiser, K. H. (1959). J. Phys. Chern. Solids 9 , 214. H u , S. M. (1977). Appl. Phys. Lett. 31, 53.

1.

INTRO1)UCTION TO OXYGEN IN SILICON

7

Hu. S . M. (1986). In Oxvgen. Carbon, Hvdrogen, und Nitrogen in Ctyvsfalline Silicon. J . C. Mikkelsen. J r . . S. J. Pearton. J . W. Corbett, and S. J . Pennycook (eds.). p. 249. Materials Research Society, Pittsburgh. Johnston. W. G.. and Gilman, J . I 1959). J. Appl. Phys. 30, 129. Kaiser. W. (1957). Phys. Ret.. 105. 1751. Kaiser. W.. Frisch. H. L.. and Reizs. H. (1958). Phys. Rev. 112, 1546. Kaiser. W.. and Keck. P. H. (1957). J . A p p l . Pliys. 28, 882. Kaiser. W.. Keck, P. H.. and Lange. C. F. (1956). Phys. Re\,. 101, 1264 Kanamori. .4.. and Kanamori. M (19791. J. Appl. Phys. SO, 8095. Keck, P. H.. and Golay. M. J . E. (1953). Phys. R e v . 89, 1297. Keck, P. H., Van Horn, W.. Soled. J . . and MacDonald. A . (1954). Rev. Sci. lnstrirni. 25,

331. Kishino. S.,Matsushita. Y . . and Kanamori. M. (1979). Appl. Phys. Left. 35, 213. Kondo. Y . (1981). I n Semiconductor Silicon 198/. H . R. Huff, R. J. Kriegler. and Y . Takeishi (eds.). p. 220. The Electrochemical Society, Pennington. N . J . Kung. C. Y.. Forbes, L.. and Peng. J . 11. (1983). Muter. R e s . Bull. 18, 1437. Leroy. B.. and Plougonven, C. (1980). J . Elecfrochem. Soc. 127, 961. Lin. W . (19%). I n Semiconductor S i l i w n 1990. H. R. Huff. K. G. Barraclough. and J. Chikawa (eds.), p. 569. The Electrochemical Society. Princeton, N.J. Maher. D. M . . Staudinger. A,. and Patel. J . R. (1976). J. Appl. Phvs. 47, 3813. Matsushita. Y. (1982).J . Crv.stal C;robt.tli 56, 516. Oehrlein. G. S.. Challou. D. J . . Jaworowski. A . E.. and Corbett. J . W. (19811. PIi!.\. Lert. 86, 117. Ohwa. M.. Higuchi. T.. Toji. E.. Watanabe. M.. Homma. K.. and Takasu. S. (1986). In Semic.onductor Silic.un l Y N 6 . H . R. Huff. T . Abe, and B . Kolbesen (eds.1. p. 117. The Electrochemical Society. Pennington. N .J. O u k a . J . , Inoue. N . , and Wada, K (1980). A p p l . Phys. L e f t . 36, 288. Patel. J . R. (1977). I n Semicondrcc~rorSilicwn lY77. H. R. Huff and E. Sirtl (eds.). p . 521. The Electrochemical Society. Princeton. N . J . Patel. J . R. (1981). I n .Srmic.ondrcc./or Silic-on l Y X / . H. R. Huff, R . J . Kriegler. and Y . Takeishi (eds.). p. 189. The Electrochemical Society. Pennington. N . J . Patel. J . R.. and Chaudhuri. A . R. (1962). J . A p p l . Phys. 33, 2223. Ponce. F. A,. Yamashita. T.. and Hahn, S. (1983). Appl. Phg.s. Lett. 43, 1051. Ravi. K. V . (1974). J . Electroc.hrrn. .So( . 121, 1090. Rozgonyi. G . A,. Deysher. R . P.. and Pearce. C . W. (1976). J . Elec,rroc.hem. So(. 123, 1910. Shimizu. H., Watanabe, 'T., and Kakui, Y . (1985). Jopun. J . Appl. Phy.5. 24, 815. Shimura. F. (1986). J . Appl. Phy.t. 5Y. 3 3 1 . Shimura. F. (19911. Solid Sirrtr Plienomentr IY-20, I . Shimura. F.. and Hockett. R. S. (1986). A p p l . Plivs. Left.48, 224. Shimura. F.. and Tsuya. H. (1982).J E/rcrroc.lirm. S ~ K 129. . 1062. Shimura. F.. Tsuya. H . , and Kawamura. T . (19XOa). J . Appl. PhyA. 51, 269. Shimura. F.. Tsuya. H . . and Kawumura. T. (I980b). Appl. Phys. Lefr. 37, 483. Sumino. K. (1981). In .Srmic.ondicc/ o r .Silic.on I Y R I . H . R. Huff, R. J . Kriegler. and Y. Takeishi (eds.). p. 208. The Electrochemical Society. Pennington. N.J. Sumino. K . . Harada. H.. and Yonenaga. I . (1980). Japtrn. J . Appl. Pliys. 19, L49. Suzuki. T.. Isawa, N . . Okubo. Y.. and Hoshi. K . (1981). I n Semiconductor Silicijn I W l , H . R. Huff. R. J . Kriegler. and Y. Takeishi (eds.), p. 90.The Electrochemical Society. Pennington. N.J.

8

F. SHIMURA

Suzuki, T., Isawa, N., Hoshi, K . , Kato, Y., and Okubo, Y . (1986). In Semiconductor Silicon 1986, H. R. Huff, T . Abe, and B. Kolbesen (eds.), p. 142. The Electrochemical Society, Pennington, N.J. Takasu, S . , Otsuka, H., Yoshihiro, N., and Oku, T. (1981). Japan. J . Appl. Phys., s ~ p p l . 20, 25. Takasu, S., Takahashi, S., Ohwa, M., Suzuki, O., and Higuchi, T. (1990). In Semiconductor Silicon 1990, H. R. Huff, K. G . Barraclough, and J. Chikawa (eds.), p. 45. The Electrochemical Society, Princeton, N.J. Tan. T. Y.. Gardner, E. E., and Tice, W. K. (1977). Appl. Phys. Lett. 30, 175. Teal, G. K., and Little, J. B. (1950). Phys. Rev. 78, 647. Usami, T., Matsushita, Y., and Ogino, M. (1984). J . Crystal Growth 70, 319. Watanabe, M., Usami, T., Muraoka, H., Matsuo, S . , Imanishi, Y., and Nagashima, H. (1981). In Semiconductor Silicon 1981, H. R. Huff, R . J. Kriegler, and Y. Takeishi (eds.), p . 126. The Electrochemical Society. Pennington, N.J. Wilson, S. R . , Paulson, M. W., and Gregory, R. B. (1985). Solid Stare Techno/. (June), 185. Yasutake, K., Umeno, M., and Kawabe, H. (1980). Appl. Phys. Lett. 37, 789. Yonenaga, I., Sumino, K., Hoshi, K . (1984). J . Appl. Phys. 56, 2346. Zulehner, W., and Huber, D. (1982). In Crystals 8: Silicon, Chemical Etching, J. Grabmaier (ed.), p. I . Springer-Verlag, Berlin.

SEMICONDIIC'IORS AND SLMIMETALS. VOL 42

CHAPTER 2

The Incorporation of Oxygen into Silicon Crystals Wen Lin ATBT BE1 I I ABORATORlkS ALLENTOWN. PENNSYLVAP,IA

1. 11.

INTRODlJCTlON

. .

9

GROWTH . . . . . . . . . . . . .

10 10 12 15

. . .

SILICON CRYSTAL

,

.

. .

.

. . . .

. .

.

.

. . . . . . . . , . . . . . . . . . . 111. CHARACTERISTICS OF CZOCHRALSKI SILICON GROWTH . . . 1 . Dopunt Distribution , , . . . . . . . . . . , . 2. "Unintended Dopunts ' ' . . . . . . . . . . . . . 3 . Eflectii.e Segrrgtrtion CoyfJicirn/ . , . . . . . , . 4. Convection F1iw.s in Czochrtrlski Melt . . . . . . . 5 . Moc,roscopic Rudiul Itnpitrity Uniformity . . . . . . 1 . F/out Zone S i l k o n Growth 2. Czochrulski Silicon GroMSth

. . .

6 . Mic.rosc.opic lnliotnogmeity in Czochralski Silicon . .

Iv.

VI.

16

19 20 21 22

OXYGFN lNCORPoRATION AND SEGREGATION IN CZOCHRALSKI SILICON

v.

IS

GROWTH . . . .

.

,

,

.

,

. .

.

.

.

,

1 . Incorporution Meclitrnism . . . . . . , . . . . 2 . Orvgen Segregrrfion trnd Microscopic Inhomogeneity

. ,

GROWTH. . . . . . . . 1 . Normu/ Czochrtr/.ski G r o ~ ~ t .h . . . . . . . . . . 2. Magnetic Field Applit,d C:ochralski Growth ( M C Z ) . 3 . Continuous C;oc hrtrl.\& Silicon Growrh . . . . . , SUMMARY . . , . . . . . . . . , . . . . . . Rejiwnces . . . . . . . , . . . , . . . . , ,

COYTROLLED OXYGkN SI1,ICON

24 24 34 37 37 42 46 50 50

I. Introduction Interstitial oxygen is perhaps the most important consideration in silicon crystals for VLSI/ULSI fabrication. The relevance of oxygen to integrated circuit fabrication is due primarily to oxygen's ability to form oxide precipitates and to generate lattice defects in a controlled manner for impurity gettering during device processing. In addition. the presence of interstitial oxygen in silicon gives an added strengthening effect to the silicon lattice, which can prevent plastic deformation and slip during wafer thermal processing. A wide range of oxygen concentrations, from 10 ppma to over 10 ppma (ASTM. 1980) in Czochralski (CZ) silicon. have been applied in IC device processing. depending on the nature of thermal 9 Copyright \C I994 hv Academic Pre\s. Inc All nghh of reproduction m any form rererved ISBN 0-I?-75?14?-9

10

WEN LIN

processing and sensitivity of the device to gettering or defect generation. In general, for device processing technologies in which gettering by precipitates is essential, high or medium oxygen concentrations are needed. When the device performance is more sensitive to lattice defects, the oxygen related defect formation is intentionally avoided by using CZ silicon that has little or no precipitation capability. In either case, an understanding of the process thermal sequence and matching oxygen level in CZ silicon is essential. The use of silicon materials with uncontrolled oxygen concentrations can result in adverse effects. To comply with the needs of integrated circuit fabrication, controlled oxygen incorporation during silicon growth is necessary. The goal has been to grow silicon at a desired oxygen concentration level with substantial axial and radial uniformity. The purpose of this chapter is to discuss how oxygen is incorporated during silicon growth and technologies for the control of concentration and uniformity. We first review the single crystal preparation by float zone and Czochralski growth methods. This is followed by a discussion of the characteristics of Czochralski silicon growth, in particular, our understanding of the oxygen incorporation mechanisms, both macro- and microscopic. Finally, the controlled oxygen incorporation is discussed in normal CZ, and their modified versions, CZ growth under applied magnetic field and continuous CZ growth. 11. Silicon Crystal Growth 1. FLOAT ZONESILICON GROWTH

The float zone (FZ) method is based on the zone-melting principle and was invented by Theuerer (1962). Figure 1 shows a schematic of the FZ process. A polysilicon rod is mounted vertically inside a growth chamber under vacuum or in an inert atmosphere. A needle-eye coil provides radio frequency power to the rod causing it to melt and maintain a narrow, stable molten zone. The levitation effect of the radio frequency field helps to support a large molten zone. As the molten zone is moved along the polysilicon rod, the molten silicon solidifies into a single crystal and, simultaneously, the material is purified. To begin the growth, in the bottom-seed FZ, the seed crystal is brought up from below to make contact with the drop of melt formed at the tip of the poly rod. A necking process is carried out to establish a dislocation-free feature before the “neck” is allowed to increase in diameter to form a taper and reach the desired diameter for steady-state body growth. During the growth, the shape of the molten zone and crystal diameter are monitored by infrared sensors,

2.

THF INCORPORATION OF OXYGEN INTO SILICON CRYSTALS

11

N=k-r Single Crystal

Seed __

FIG. I . Schematic of a floa~Lone silicon growth arrangement

and they are adjusted by the rf power input to the coil and travel speed. Details of FZ technology are discussed by Keller and Muhlbauer (1981). Current FZ technology can produce high-quality FZ silicon up to 150 mm in diameter in production quantities. FZ crystals are doped by adding the doping gas phosphine (PH,) or diborane (B,H,) to the inert gas for n- and p-type, respectively. Polysilicon rods for FZ growth may also be doped in the gas phase and dopant redistribution by zone melting. Since the doping is by gas phase interaction with the molten silicon, axial dopant uniformity is achieved. However, due to the very nature of FZ growth configuration, the small "hot zone" lacks thermal symmetry. As a result, temperature fluctuations, remelting phenomenon and dopant segregation cause FZ silicon to display more microscopic dopant inhomogeneity or dopant striations than that observed in the CZ silicon. Severe dopant microinhomogeneity can be improved in n-type FZ via NTD (neutron transmutation doping) (Meese, 1979). In NTD, a high-purity (undoped) FZ crystal is subjected to thermal neutron bombardment, causing some of silicon isotope '"Si (-3.1%' of Si) to form unstable isotope "Si, which decays to form stable phosphorus isotope 3'P, such that '"Si(n, y )

- "Si

j'P

+

p

(7.6 hr)

Since neutron bombardment (hoth thermal and fast neutrons) induces radiation damages, the irradiated crystal must be annealed at about 700°C for defect annihilation and to restore resistivity due to the phosphorus doping. In the FZ silicon with NTD. the dopant striations are greatly reduced. However, the NTD method is feasible only for high-resistivity,

12

WEN LIN

phosphorus-doped FZ. Low-resistivity doping of FZ by NTD would require excessively long irradiation (more lattice damages) and is not feasible. The NTD process for the p-type doping is not available. Unlike CZ growth, the silicon molten zone in the FZ growth is not in contact with any substances except ambient gas, which may contain doping gas. Therefore, the F Z silicon can easily achieve much higher purity and higher resistivity (FZ silicon’s resistivity ranges from few tens to a few thousands ohm-cm) than the CZ silicon (generally, 9OO0C). In the growth of ( 1 11) and (100) crystals, the growth axes are oblique or perpendicular to { 1 1 I} slip planes. The dislocations can glide out of the crystal surface at some time. For ( 1 10) growth, because ( I 10) is contained in a { I 1 1) plane, the seed has to be oriented a few degrees off the pulling axis toward the direction perpendicular to the ( I 11) plane, to facilitate dislocation eliminations. When the neck is 3-4 mm in diameter under high-speed pulling, the stress is relatively small, causing slow or no movement of the prevailing dislocations. When dislocation movement is slower than the advancing solid-liquid interface, the dislocation-free feature is obtained. Typically, the dislocation-free status is accompanied by the

2.

THE I N C O R P O R A T I O N O F O X Y G E N INTO SILICON C R Y S T A L S

15

growth of strong ridges (( 100) crystals) or “flats” (( I 1 1) crystals) on crystal’s symmetry positions. which are actually due to prominent { 1 I I } facet growth at these positions (Lin and Hill, 1983a). Once dislocation-free growth is achieved through the necking. the diameter may be expanded by “shoulder” growth until it reaches the desired diameter. The body growth is under automatic diameter control (ADC). in which the pull rate is slaved by optically monitored crystal diameter variations. The ADC is also assisted by minor temperature adjustments slaved by the long-term pull rate changes. The crystal growth process is terminated by a gradual decrease from full diameter to zero in a low pull speed in order to minimize thermal stress by the diameter change and associated slip generations. After the heater power is off, the crystal usually stays in the grower for a period of time for cooling before it is removed from the grower. The total dwell time and temperatures that crystal experienced in the grower constitute the so-called thermal history of the silicon crystal. The thermal history of CZ silicon determines the state of nuclei for oxygen precipitation and is an important consideration. as is oxygen concentration, in oxygen precipitation kinetics. The heart of a CZ puller is the hot zone. The design of heater and heat shields, for example, will determine radial and vertical thermal gradient in the melt. These thermal characteristics are intimately related to the growth characteristics, such as interface shape and related thermal stress generation (Lin and Benson. 1987). Although this concept is fundamental to large-diameter silicon growth. little is known about the correlation between crystal growth system hot-zone design factors and growth characteristics. Empirically, for a given growing system an optimum growth condition is usually obtained by modifying hot-zone components or by varying the growth parameters by trial and error. Hot-zone thermal characteristics affect many aspects of silicon crystal properties including oxygen incorporation behavior and the thermal history of the grown crystal. Since hot-zone design varies from one grower to another. the crystals grown from different growers are expected to differ in these properties. Thermal convection and forced convection conditions are also important controlling factors for CZ crystal properties and will be discussed in the following section. 111. Characteristics of Czochralski Silicon Growth

I . DOPANT DISTRIBUTION

In the growth of silicon crystah from large melts using automatic diameter control mechanisms involving pull rate or temperature changes

16

W E N LIN

slavea to optical diameter measurements, the axial dopant distributions follow the normal freezing behavior (Pfann, 1965), that C,(X) = Co k (1

-

x)’-~,

(1)

where C,, k and x are crystal dopant concentration, dopant segregation coefficient and fraction of melt solidified, respectively. C, is the initial dopant concentration of the melt. Complete mixing takes place in the melt by vigorous thermal convection, and the segregation coefficient of the dopant assumes equilibrium value k , in most instances. In the reduced pressure growth of heavily doped silicon involving dopants with high vapor pressure, such as antimony, the k value can deviate significantly from the equilibrium value (k assumes a value greater than k,). Due to dopant segregation, there is a spread in dopant concentration along a CZ crystal. The degree of the spread depends on the k value of the dopant. The smaller is the k value, the larger the spread in concentration. The segregation effect of the dopants often limits the “yield” of the CZ silicon crystals. Nonstandard CZ methods, such as double crucible method (Benson, Lin and Martin, 1981; Lin and Hill, 1983a) and continuous growth method (Fiegl, 1983) have been used to eliminate the effect due to segregation, see Fig. 3. The axial microscopic uniformity is controlled by the microscopic growth rate. Thermal convection, thermal asymmetry and pull-rate fluctuations are sources of microscopic growth fluctuations. The nature of the microinhomogeneity of impurity in CZ crystals will be discussed following the discussion of melt convection flows and effective segregation coefficient. 2. “UNINTENDED DOPANTS” Impurities in the crucible material or the vapor above the melt can first be incorporated into the melt and then, the silicon during crystal growth. Oxygen and carbon are the major impurities incorporated into CZ silicon. Their concentrations in CZ crystals are on the order of 10l8 atoms/cm’ and 10l6atoms/cm3for oxygen and carbon, respectively. The silica crucible is an infinite source for oxygen. Molten silicon dissolves the silica and absorbs oxygen. Unlike normal dopants, oxygen in the silicon melt is a dynamic system and oxygen distribution is not homogeneous in the melt. The oxygen concentration incorporated into the crystal is a result of complex interaction between functions such as crucible dissolution rate and nature of the fluid flow (which determines how the oxygen-rich melt is transported). Therefore, the axial oxygen profile of a silicon crys-

2.

THE INCORPORATION OF OXYGEN INTO SILICON CRYSTALS

17

CAPILLARY

INNER CRUCIBLE

MELT

OUTER CRUCIBLE

L A.-.....-!-* Meltdown Inner Crucible

Chamber

(b) FIG. 3 . ( a ) Schematic representation of a double crucible growth arrangement (after Benson et al. 1981: the paper was originally presented at the spring 1981 meeting of the Electrochemical Society. Minneapolis). (h) C.'ontinuous liquid-feed Czochralski growth furnace (after Lorenrini, Iwata and Lorenz 1977).

18

WEN LIN

tal is not the result of normal freezing behavior and concentration profile can vary widely depending on the grower thermal characteristics and growth parameters used. The source of the carbon is the graphite material making up the hot zone of the grower. The silicon monoxide evaporated from the melt surface interacts with hot graphite components and is reduced to carbon monoxide before re-entering the melt following SiO

+ 2C

-

Sic

+ CO.

The introduction of CO into the melt is a continuous process. The incorporation from vapor phase and residual carbon content in the starting polysilicon (elineation of Defects in Silicon." J . Electrochem. So(.. 13115). 1140.

Yao. K. H.. and Wilt, A. F. (1987). "Scanning Fourier Transform Infrared Spectroscopy of Carbon and Oxygen Micro\egregation in Silicon." J . C'rvsr. Growrh 80, 453. Yatsurugi. Y.. Akiyama, N., Endo. Y . . and N o u k i . T. (1973). "Concentration. Solubility, and Equilibrium Distribution Coefficient of Nitrogen and Oxygen in Semiconductor Silicon." J . Elrc!rochern. SO( 120(7).975. Yuezhen, L., and Qimin, W . (1985). "Keview o f the Accurate Determination of Oxygen in Silicon." In R e t ~ i e ~ofv Progrt,.q.\ in Quunrilutitv iVondesrrucrive Evuluution. p. 957. Plenum Pres\. New York. Zaumseil, P., Winter, U.. Servidori. M . . and Cembali. F. (1987). "Determination of Defect and Strain Distribution in Ion Implanted and Annealed Silicon by X-Ray Triple Crystal Diffractometry." In G I t r e r i n g r ~ t i d1)qfec.r Engineering in Semiconducror Tec,hno/og.v, H . Richter (ed.). p. 195. GADEST '87. Acad. Sci., Germany. ,

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S E M I C O N I I I I ( ' I O K S A N D SEMIMETALS. VOL. 42

CHAPTER 4

Oxygen Concentration Measurement W . M . Bullis MATERIALS & METROLOGY 5CrNNYVALP. CALIFORNIA

1. 11.

INTRODUCTION . . . . . . . . . . . . . . . . . . INFRARED ABSORPTION Mt ~ S I I R E M F N T SUNDERI D ~ A I . CONDITIONS . . . . . . . . . . . . . . . . . . . . 111. I N F R A R E D S P E C T R O M t l t R S . . . . . . . . . . . . . I . 1)i.spersii~eIqfrurc,tl .Spr,c-trometrr.s . . . . . . . . . 2. Fourier- Trun.\,fo,-iti-lnfr(irc,d S p c ~ t r o r n e t e r s . . . . . . Iv. A N A IYSlS OF O X Y C l tw SPEC TKA . . . . . . . . . . . . . I . Busc~linr~ . . . . . . . . . . . . . . . . . 2. Anuly.sis M e t h o d . Pcul / f r i g h t o r Intrgrutcd Areti! . . 3 . Multiple Refiec.ti~intint/ Interf>,rrnce Fringes . . . . . 4. SpcJc,trirmCollec l i o n Method: A i r Rqf'erence or LXflerence? . . . . . . . . . . . . . . . . . . 5. Rc IS"C/min) to room temperature (Jastrzebski et al., 1982). +

1. CALIBRATION FACTORS FOR ROOM TEMPERATURE MEASUREMENTS

Many workers have reported the results of experiments to obtain the calibration factor for oxygen absorption at room temperature. These are

4.

OXYCitN

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O N C t N T R A T I O N MEASUREMENT

137

summarized in Table V1. The table lists the number of data points used in developing the calibration factor, the error range specified for the infrared and chemical measurements, the sensitivity limit of the chemical method, the range in oxygen content of the samples used as determined by the chemical method (converted to ppma, if reported in atoms/cm’), and the reported calibration factor. Blank spaces indicate that no information was supplied in the paper. Calibration factors in parentheses were xaled from published graphs, and those in brackets were computed from published data tables. The temperature of the measurement was not indicated in most cases. Barraclough et al. (1986) indicate that their value was obtained at 30°C. Murray et al. ( 1992) conclude that both their value and IOC-88 (Baghdadi et al.. 1989) are referenced to 310 K (37°C). In view of the relatively small temperature coefficient of aOx( - 0.16%’/”C), the systematic error introduced by neglecting the temperature variation over the temperature range 295 t o 3 15 K (22 to 42°C) is on the same order of magnitude as observed multilaboratory measurement reproducibility (Murray et al., 1992). In the initial determinations of oxygen in silicon (Kaiser, Keck, and Lange, 1956; Kaiser and Keck, 1957) vucuum fusion analysis (VFA) was used as the basis of calibration* for the infrared measurements. In this method, the silicon sample is etched in concentrated H F to remove the surface oxide and then melted in a graphite crucible containing liquid iron at 1700°C. forming carbon monoxide, which is detected in a gas analyzer. The claimed accuracy of this technique is 5 2 x lo” oxygen atomsicm’. I n this technique, which was also used by Graff et al. (1973). care must be taken to avoid interference from oxygen in the surface oxide, since any such oxygen is also detected in the instrument. lnerr gus$uion analysis (IGFA) is a similar technique except that the vaporized sample is transported with an inert gas, usually helium. Baker (1970) used this method as the basis of calibration in his study. The results were widely scattered but the resulting calibration curve was accepted for many years (see Section V l ) . The group at the Shanghai Institute of Metallurgy (He et al., 1983; Li and Wang. 1985) extensively refined the IGFA technique, taking great care to prepare samples with smooth surfaces. replacing the iron with nickel-tin to improve the extraction of *‘There is some confusion over the actual value of the calibration factor found by Kaiser and Keck. The value found IS not quoted in the paper. The value given in the table ( 5 . 6 ) was scaled from the published plot of oxygen by VFA against the measured absorption coefficient at I107 c m I. Pajot (1977) quotes a value of 5.7, Baker (1970) quotes a value of 5.76. and the slope of the graph published in the early ASTM standard (ASTM. 1964) is 5.45.In this chapter, the Kaiser and Kecli calibration factor is taken as 5.6 unless otherwise noted.

F

TABLE V1

w

00

OF CALIBRATION FACTOR EXPERIMENTS SUMMARY

Source

Chemical Method(s) Used

No. of Data Points

Kaiser and Keck (1957) Iglitsyn, Kekelidze, and Lazaeva (1965) Aleksandrova et al. (1967) Rook and Schweikert (1969) Kim (1969. 1971) Baker (1970) Gross et al. (1972) Yatsurugi et al. (1973) Graff et al. (1973) Abe et al. (1983) He et al. (1983) H e et al. (1983) Iizuka et al. (1983, 1985) Rath et al. (1984) Chu, Hockett, and Wilson (1986) Barraclough et al. (1986) Regolini et al. (1986) Baghdadi et al. (1989) Murray et al. (1992)

VFA LD CPAA CPAA CPAA IGFA CPAA CPAA VFA CPAA IGFA CPAA CPAA PAA SIMS PAA CPAA CPAA, PAA CPAA, PAA

12 8 3 4 6 99 4 12 8 67 7 22 8

2 21 8 20 6

Stated Error (infrared)

Stated Error (chemical)

Sensitivity Limit, ppma (chemical)

5 4 ppma

10% 20% f 3 ppma 3 R cm; nominal oxygen concentrations were 17, 23, and 26 ppma (IOC-88). The reference specimen was cut from a float-zoned crystal with oxygen concentration less than that quoted for BCR CRM 368. Comparison measurements were made with test specimens evaluated in the international oxygen round robin experiment (Baghdadi et al., 1989) in order to establish the oxygen concentrations. In conducting the certification measurements, emphasis was placed on spectrometer reproducibility rather than on the uncertainty in the oxygen determination. The single-beam difference method was employed and the determinations were made from analysis of the peak heights of absorption spectra suitably corrected for multiple-reflection effects. The measurements were made on a Model MB-100 Bomen FT-IR spectrometer, a small instrument with very rigid construction, which is important for achievement of high precision. Resolution of 4 cm-’ and a 2-mm diameter

*

4. O X Y G E N

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ON( L N T R A rlON MEASUREMFNT

147

DTGS room-temperature detector were used. The specimens were located 50 mm behind the focal point of the optical beam and the beam diameter at the sample position was 5 mm. A light cone was placed in front of the detector to eliminate errors due to spatial nonuniformities of the detector response. This nonuniformity was found to be the largest single source of measurement imprecision. N o effects that could be attributed to the emissivity problems noted in the BCR study (Murray et al.. 1992) were observed. The precision of the FT-IR measurements was found to be about 0.15% as compared with the 6% uncertainty in the absolute determinations. The same instrument and analysis procedures were applied to a BCR CRM 369 set; results obtained were within 1%' of the stated oxygen concentration. V11. Summary

Routine measurement of oxygen in silicon can be accomplished with state-of-the-art Fourier-transform or dispersive infrared spectrometers on silicon wafers that are not too heavily doped. However, there is still some disagreement as to values obtained from different instruments and on samples with different surface preparation. Despite the recent appearance of certified reference materials for this determination and the recent revisions of the DIN standard test procedure, some additional standardization effort remains to be completed, both for the infrared absorption and the routine chemical methods. Activity is now in progress in Japan, within the Silicon Wafer Committee of Semiconductor Equipment and Materials International (SEMI). to develop a standard test procedure for the Brewster angle method (Shirai, 1991, 1992). Further work is required on the ASTM standards to extend them to single-side polished wafers and to account for the nonnormal incidence angle of modern FT-IR spectrometers. Further development of the SIMS method is also required to provide procedures for assuring that the wafers used for calibration meet the desired uniformity characteristics. The existing standard test method for oxygen uniformity (ASTM, 1985) provides sampling plans that are too coarse for this application. In addition, development of a standard method for IGFA would be a useful addition to the standards literature. A(XNOWI.EIX;MENTS The author would like to acknouledge u5eful divxssions with many individuals on various aspects of oxygen measurements in vlicon over the years. including A. Baghdadi. B. Rennex. and K. I . Scace of NIST. M . Kulkarni of IBM. K . Krishman of BioRad. K. Graff

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of Telefunken Microelectronic, R. Boyle and J. Steele of Nicolet, M. Watanabe of Toshiba ULSI Laboratory, Y.Li of Shanghai Institute of Metallurgy, R. Series and K. Barraclough of RSRE. He would also like to thank K. Graff, B. Pajot of UniversitC Paris VII, and R. Murray of Imperial College for a preprint of their article on the BCR study and K. Nishikida of Perkin Elmer and R. Boyle for furnishing illustrations of infrared spectrometers.

REFERENCES Abe, T., Gotoh, S., Ozawa, N., and Masui, T. (1983). In Silicon Processing, ASTM STP 804, D. C. Gupta (ed.), pp. 469-476. ASTM, Philadelphia. Aleksandrova, G. I., Demidov, A. M., Kotel’nikov, G. A,, Pleshakova, G. P., Suhov, G. V . , Choporov, D. Y., and Shmanenkova, G. I. (1967). Atomnayu energiya 23, 106-109 [in Russian]. ASTM. (1964). “Tentative Method of Test F 45 for Oxygen Content of Silicon.” (Discontinued 1970.) ASTM. (1970a). “Standard Practices F 120 for Determination of the Concentration of Impurities in Single Crystal Semiconductor Materials by Infrared Absorption Spectroscopy.” (Revised completely in 1987; see ASTM, 1987.) ASTM. (1970b). “Standard Test Method F 121 for Interstitial Atomic Oxygen Content of Silicon by Infrared Absorption.” (Note-In 1980, the calibration factor between peak absorption at 1107 cm-’ and the interstitial oxygen content used in this method was changed from 9.63 ppmalcm-’ (old ASTM) to 4.9 pprnalcm-’ (new ASTM or DIN). Discontinued in 1990.) ASTM. (1985). “Standard Test Method F 951 for Determination of Radial Interstitial Oxygen Variation.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. ASTM. (1987). “Standard Practices F 120 for Determination of the Concentration of Impurities in Single Crystal Semiconductor Materials by Infrared Absorption Spectroscopy.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. (Note-These practices were revised completely in 1987; to distinguish between the two standards, a new citation is placed here. The background material on multiple reflections was inadvertently lost in the revision: it was returned to the standard in 1988 as Appendix XI.) ASTM. (1988a). “Standard Test Method F 1188 for Interstitial Atomic Oxygen Content of Silicon by Infrared Absorption.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. ASTM. (1988b). “Standard Test Method F 1189 for Using Computer-Assisted Infrared Spectrophotometry to Measure the Interstitial Atomic Oxygen Content of Silicon Slices Polished on Both Sides.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. ASTM. (1989). “Standard Test Methods F1239 for Oxygen Precipitation Characterization of Silicon Wafers by Measurement of Interstitial Oxygen Reduction.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. ASTM. (1992a). “Standard Test Method F 398 for Majority Carrier Concentration in Semiconductors by Measurement of Wavenumber or Wavelength of the Plasma Resonance Minimum.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. ASTM. (1992b). “Standard Test Method F 1366 for Measuring Oxygen Concentrations in

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Heavily Doped Silicon Substrate\ by Secondary Ion Mass Spectrometry.“ Annitul Book qf A S T M Stondurds. Vol. 10.05. Published annually by ASTM. Philadelphia. Baghdadi, A. (1984). In Semicondut / o r f’roc.rs.\inR, ASTM S T P 850. D. C. Gupta ( e d . ) , pp. 343-357. ASTM. Philadelphia. Baghdadi. A , . Bullis. W. M . . Croarhin. M. C . . Li Yue-zhen, Scace. R. I.,Series, R. W.. Stallhofer. P.. and Watanabe. M. 11989). J . Elt,c/rochem. Soc. 136, 2015-2024. Baghdadi. A , . and Gladden. W. K . (19x5). Proc. SPIE 553, 207-209. Baghdadi. A.. Scace. R. 1.. and Walters. E . J . (1989). ”Semiconductor Measurement Technology: Database for and Statistical Analysis of the lnterlaboratory Determination of the Conversion Coefficient for the Measurement of the Interstitial Oxygen Content of Silicon by Infrared Absorption ’ ’ N I X Spec. Publ. 400-82. Baker. J . A. 11970). Solid-Stare Elec.trorric .s 13, 1431-1434. Barraclough. K . G., Series, R. W.. Hislop. J . S.. and Wood. D. A. (1986). J . Elecrrochc~m. S o c . 133, 187-191. Birch. J . R.. and Nicol. E . A . (1987). Intrcirc~dPlrys. 27, 159-165. Bleiler. R. J . . Chu, P. K . . Novak. S. W . . and Wilson. R. G . (1989). In Proc. SIMS V I I . A. Henninghoven, C. A . Evan\. K. I). McKeegan. H . A. Storms. and H . W. Werner ( e d s . ) . pp. 507-510. John Wiley &L Sons. New York. Bleiler. R. J . . Hockett. R. S.. Chu. P.. and Strathman. E. (1986). In Oxvgen, Ctrrhori. H v t l r o g r n uncl Nirrogen in Ct?..\rtrlliiic. Silic.ori. Mat. Res. Soc. Symp. Proc. V o l . 59, J . C . Mikkelsen. Jr.. S . J . Pearton W. C‘orbett. and S. J . Pennycook (edb.). pp. 73-79. Materials Research Society. Pitt\burgh. Bosomworth. D. R.. Hayes. W., Spray. A. R. L . , and Watkins. G . D. (1970). Pro.” NIST Spec. Publ. 400-81. includes 5 % in. disk. Goldstein. M.. and Makovsky. J . I 1080). I n Surnic,ondrrcror Fohricution: TechnoloRy ond Merrology. ASTM STP 990. D C . Gupta ( e d . ) .pp. 350-360. ASTM. Philadelphia. Graff. K . (1983). J . Electrochc~m.S o ( . 130. 1378-1381.

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C. A. Evans. K. D. McKeegan. H . A . Storms. and H . W. Werner (eds.), pp. 487-490. John Wiley & Sons. New York. Murray. R.. Graff. K.. Pajot, B . , Stri,jckmanr, K.. Vandendriessche. S . , Gnepink, B . . and Marchandise. H . (1992). J . Elecrrochc.m. Sot.. 139, 3582-3587. Neuhrdnd. H . (1973). Phvs. Stiit. Sol. ( t i ) 17. 459-470 [in German]. Nozaki. T.. Yatsurugi. Y., Akiyama. N . . Endo. Y . . and Makide. Y . (1974). J . Rndiounul. Chem. 19, 109-128. Oates. A. S . . and Lin, W. (1988).J . C r w t u l G r o ~ 3 r h 8 9 ,117-123. Pajot. B. (1977). Analitsis 5, 293-303 Pajot. B . . and von Bardeleben, J . (19x4). In Thirreenth Internutionnl Conference on Dyfects in St,,nicondrrc.ror.\. L. C . Kimerling and J . M . Parsey. Jr. (eds.), pp. 685-691. The Metallurgical Society of AIME. Warrendale, Pa. Pajot. B . . and Cales. B. (1986). In O a v x c t i . C’urbon. Hvdrogrn und Nitrogrn in Cryvstolline .Silicoti, J. C. Mikkelsen. Jr.. S . J . Pearton, J . W. Corbett. and S. J . Penneycook (eds.), MRS Symp. Proc. Vol. 59, pp. 39-44. Materials Research Society. Pittsburgh. Pajot. B . . and Deltour. J . P. (1967). Iri.frtired P l i v s . 7, 195-200 [in French]. Pajot. B . , Stein, H . J . . Cales. B . . and Nitud. .. and Schmitt. B. F. (1984).J. Electrochem. Sot.. 131, 1920-1923. Rath. H . J.. Keffle. J . . Huber. D., Eichinger. P . . Iberl. F . , and Bernt. H . (1985). In Impuritv Diffir.sion und Getterinfi i n S i / i < o t i , Mat. Res. Soc. Symp. Proc. Vol. 36, R. B. Fair. C. W . Pearce. and J . Washburn (eds.). pp. 193-198. Materials Research Society. Pitt5burgh. Regolini. J . L., Stoquert. J . P., Ganter. C . , and Siffert, P. (1986). J. Electrochem. Soc. 133, 2165-2168. Rennex. B. ( 1994). “The Certification ot a Standard Reference Material for the Determination of Interstitial Oxygen Concentration in Semiconductor Silicon by Infrared Spectrophotometry.” NlST Spec. Publ. 260-1 19. Rook. H. L.. and Schweikert. E , A . (1969). A n t i / . Chem. 41, 958-963. Schomann. F..and Graff. K . (1989). J . E/ec,/roc-lir.m.Soc. 136, 2025-2031. Schroder. D. K.. Thomas. R. N and Swartz. J . C. (1978). IEEE T r a n s . Electron Devices ED-25, 254-261. Schumann. P. A , . Jr., and Phillips, K . P. (1967). Solid-Stute Electronics 10, 943-948. Schumann. P. A , . Jr.. Keenan. W. A , . Tong, A . H . , Gegenwarth, H. H., and Schneider, C. P. (1971). J . Electrochem, S o c . . 118, 145-148. Schweikert, E. A,. and Rook. H. L. (1970).Anul. Chern. 42, 1525-1527. Schwenk. H . (1987). Unpublished internal report. Wacker Chemitronic. Burghausen, Germany. (Cited in Schomann and Graff. 1989.) Series. K. W. (1982). “Determination of Oxygen and Carbon in Silicon.’’ RSKE Memorandum No. 3479, Royal Signals and Radar Establishment. Malvern. Worcs.. U.K. Series. R. W., and Griffiths. D. P (1986). E/t,c.rrochem. Soc. Extended Abstructs & ( I ) . Abstract 251. Series. R . W., and Livingston. F. M . (IYH6J.Elec~rrodiem.Soc. Extended Abs/ruct.s 86(1). Abstract 250. Shimura. F.. Ohnishi. Y . , and Tsuya. H. (1981). Appl. Phvs. L e t t . 38, 867-870. Shirai. H . (1991). J . Elec,trochem. S C K . 138, 1784-1787. Shirai, H . (1992).J . Electrochem. S C K . 139, 3272-3275.

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SEMICONDCIC IOKS A N D S E M I M E T A L S , VOI. 42

CHAPTER 5

Intrinsic Point Defects in Silicon S.M .

Hu

IBM SEMICONDUCTOR RESEAR( H AND DFVELOPMENT CENTER EAST FISHKII.1 FACII ITY. H O P r W E l 1 JUNCTION, NEW YORK

I. INTRODUCTION . .

. .

. . . . . . . .

. . .

. .

DEFECTMANIFESTATION O F INTRINSICPOINT DEFECTS 11. SWIRI. DEFECTSI N SII.I( ON . . . . . . . . . . . . . 111. THERMAL 1v.

SELF-DIFFUSION

. .

.

. . . . .

. . . . .

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.

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I . Point Defecrs and Se/f’IAflir.sion . . . . . . . . . . 2. SelfDi’jJision ,from Isorope Experiments . . . . . . . 3 . SelflDiffusion frowr Kinericy of Extended Defects . . . V . COEXISTENCE OF VA(ANCIF s A N D SEXF-INTERSTITIALS IN SILICON . . . . . . . . . . . . . . . . . . . . . . VI. INTERSTITIALCONFIGURATIONS A N D CHARGE-ENHANCED MIGRATION . . . . . . . . . . . . . . . . . . . . I . Ceomerrical Configrirtrrions nntf Migration Puthhwvs of the .Self-fntersritiirl . . .

. . . .

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i53 i56 159 160 160 161

162 164 166

166

2. Charge-Enhanced trnd Arhi~rmulMigration oj‘the Self-fn/rrsririul

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VIII.

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FORMATION A N D MILRATION PARAMETERS OF POINTDEFECTS I . Stitdies of’ Point 1)t:f’ec.t~front Irradiations . . . . . . 2. Vaciinq Fortna/ion Energy ,from Positron-Lijerime

170 172

172

Measurements . . , . . . . , . . . . . . . . . . 3 . Point Dyfec.1 Conc.c.titrtirion.(,from Thermal E-vpansion . . . , , , . . . . . . . . Mensurement5 . . . 4. Estimation of Se/f-lnter.stiriu/ Concentration ,from Oxygen Precipirtrtioti . . . . . . . . . . . . . . . 5 . Diffirsivity qf thc Se!f~lnter.sririul,from Membrane Experiments . . . . . . . . . . . . . . . . . . 6 . Defect Parumetc~rs,from Mode/-Fitting Au and PI

17.5

Diffusion . . . . . . . . . . . . . . . . . . . . DEFECTENERGETICS A N D PATHWAYS FROM THEORETICAL CALCUI.ATIONS . . . . . . . . . . . . . . . . . . S UMMARY . . . . . . . . . , , . , . . . . . . .

17X

Rqfirences

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. . . .

175

176 177

179 184 185

I. Introduction

Point defects affect many fundamental as well as technologically important phenomena in crystalline solids. Of their many roles, the best known I53 Copyright 0 1994 by Academic Presa. Inc. All nghtr of reproduction in any form reserved. ISBN 0-12-752142-9

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is that of acting as vehicles of atomic transport processes such as diffusion and certain activated processes such as the dynamics of solid deformation. They also serve as progenitors of extended crystalline defects such as point defect clusters, stacking faults and dislocations, which are harmful to semiconductor devices. Of particular interest to the reader of this book is their role in oxygen precipitation and vice versa. In 1977, it was accidentally discovered (Hu, 1977b) that oxygen precipitation is retarded when silicon specimens are annealed in oxidizing ambients. A subsequent detailed investigation confirmed this phenomenon (Hu, 1980a). It had by that time already been established (Hu, 1974) that thermal oxidation of silicon causes excess self-interstitials to be injected into the silicon substrate. Together with the well-known fact that the agglomeration of interstitial oxygen atoms into SiO, precipitates produces local strain, it was proposed (Hu, 1980a) that oxygen precipitation can be modeled by the reaction 2x0,

+ ySis GS

xSi0,

+ (y

-

x)Si,,

where the subscript I indicates an interstitial configuration. An excess of silicon self-interstitials causes this reaction to shift to the left, consequently retarding the precipitation. Various experimental observations have since confirmed the precipitation-retardation effect of oxidizing ambients (Schaake, Barber, and Pinizzotto, 1981; Craven, 1981; Oehrlein, Lindstroem, and Corbett, 1982; Tan and Kung, 1986). Conversely, oxygen precipitation may cause the generation of self-interstitials, as given in the forward direction of the reaction. This prediction has also been confirmed by observations of the growth of stacking faults (Hu, 1980b; Rogers et al., 1989; Rogers and Massoud, 1991a; Shimura, 1992) and the enhanced diffusion of phosphorus and the retarded diffusion of antimony (Kennel and Plummer, 1990) accompanying oxygen precipitation. In silicon heavily doped with antimony, the precipitation of oxygen has been found to be retarded (de Kock and van de Wijgert, 1981; Tsuya, Kondo, and Kanamori, 1983; Shimura et al., 1985). Various explanations have been proposed. One explanation (Wada and Inoue, 1986; Bains et al., 1990; Gupta et al., 1992) is that the oxygen thermal donor is the precursor of an embryonic precipitate (Ourmazd, Schroter, and Bourret, 1984), and that the rate of formation of thermal donor is reduced by a high electron concentration (cc n - * ) (Wada, 1984). Other explanations invoke the roles of point defects in precipitate nucleation (de Kock and van de Wijgert, 1981; Shimura et al., 1985). For example, it was suggested (Shimura et al., 1985) that the suppression of oxygen precipitation may be caused by the complexing of lattice vacancies with antimony atoms,

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thereby reducing the availability of vacancies required for precipitate nucleation. Diffusion in silicon has been extensively investigated since the mid 1950s. Until 1968, it had always been assumed, implicitly or explicitly, that the point defect that mediates diffusion in silicon is the vacancy. A “regular” interstitial is conceptually one that wanders through lattice interstices all by itself without displacing lattice or substitutional atoms. But diffusion by an interstitiu/(.y mechanism was already suggested by Seitz (1950). Seitz was discussing generic diffusion without reference to specific materials. Experimental diffusion data in metals tend to indicate a preponderance of the vacancy mechanism. Seeger and Chik (1968) argued that self-diffusion in silicon at high temperatures. as well as diffusion of group 111 and V dopants, most likely proceed via an interstitialcy mechanism rather than a vacancy mechanism. But no unequivocal experimental evidence was given in support of this speculation. Hu (1974) proposed that both vacancies and self-interstitials actually coexist as two basic intrinsic point defects in silicon of essentially equal importance and that diffusion of substitution impurities in silicon proceed via a dual vacancy-interstitialcy mechanism. The contribution of the interstitialcy mechanism as a fraction to the total diffusivity varies with dopant species. Hu arrived at this conclusion by bringing together the phenomena of enhanced diffusion and generation of stacking faults in the thermal oxidation of silicon, and analyzing their common features and causal relations such as the effects of surface orientation and oxidizing ambients. A second proposition was made at the same time that thermal oxidation generates excess silicon interstitials. This proposition is essential for the experimental observation of the oxidation enhanced diffusion (OED) and the formation of oxidation stacking faults (OSF). In a later section, we will discuss the facts and the reasoning leading to this conclusion. Since then, many phenomena have been discovered which have been explained very well by this model. Most of these phenomena are related to the discoveries of additional sources of generation of nonequilibrium point defects and their annihilation. Some sources generate excess vacancies, while others generate excess self-interstitials, affecting the diffusion of different dopants in different ways according to the dopants’ characteristic interstitialcy components. Knowledge about the relative contributions of the vacancy and the interstitialcy to the diffusion of a dopant becomes crucial for the prediction of diffusion profiles in presence of nonequilibrium point defects. Many of these phenomena have been discussed very thoroughly in a recent review by Fahey, Griffin. and Plummer (1989a). Two other fairly recent reviews (Frank et al., 1984; Hu, 1985) should also be of interest to the reader.

156

s. M. HU 11. Swirl Defect Manifestation of Intrinsic Point Defects

As a new part of a silicon crystal is freshly grown from a melt, it contains equilibrium concentrations of vacancies and self-interstitials, as well as their complexes. As that part of the crystal moves away from the melt and becomes colder, the majority of these grown-in point defects become excess over their new equilibrium concentrations at a lower temperature, and are subject to population reduction. In a crystal that is substantially dislocation free, the only avenues open to their depopulation are the vacancy-interstitial annihilation, and the agglomeration among like species themselves into extended defects. This is in contrast to the fate of excess point defects in thin silicon wafers, in which they can depopulate, beside via vacancy-interstitial annihilation in the bulk, by escaping to the wafer surface and thereby vanish. (We should note, however, that the occasional presence of nucleation centers, typically stress centers, may induce the excess point defects to agglomerate, even in thin wafers, into extended defects. A prime example is the formation of oxidation stacking faults.) These more macroscopic microdefects, as they are commonly called, can readily be examined visually by a number of techniques such as preferential etching, copper-decoration, and transmission electron miscroscopy (TEM). These microdefects are usually distributed throughout a crystal in a striated pattern, due to the nonuniformity in the temperature field in the crystal growth environment in which a crystal rotates during growth. As the solid-melt interface is usually concave, the distribution of these microdefects on a flat-cut surface of a wafer exhibits swirl pattern from preferential etching. For this reason, these microdefects are also referred to as swirl defects. Plaskett (1965) first reported the occurrence of what were thought to be clusters of vacancies in the inner region of a silicon crystal. The width of the cluster-free outer ring of a wafer cut from the crystal is about 1.5 mm, which was thought to be indicative of the vacancy diffusion length in the temperature transient during the growth. Abe, Samizo, and Maruyama (1966) first reported the distribution of shallow etch pits of microdefects in swirl patterns. Swirl defects were first studied in detail by de Kock (1973). He noted two kinds of such microdefects, which he termed type A and type B. These were conjectured to be clusters of point defects or clusters of complexes of impurities and point defects. A-defect is, relatively speaking, quite large and can be readily examined by TEM. Subsequently, FOll and Kolbesen (1975) identified the A defects as an interstitial type dislocation loops. From this observation, they proposed that the dominant intrinsic point defect in silicon is the self-interstitial. The A defects would form from the agglomeration of excess self-

5

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interstitials that had been left after vacancy-interstitial annihilation. The B-defect could not be characterized by TEM; but such defects can be revealed in their spatial distribution by means of selective etching or metallic decoration. Hu (1977a) suggested an alternative model of swirl defect formation: The excess vacancies and self-interstitials do not annihilate completely, and significant fractions of the excess populations of both species agglomerate, separately and in parallel, into the A- and the B-defects. The larger A-clusters are agglomerates of self-interstitials in the form of dislocation loops ( interstitial-type disks), while the smaller B-clusters, as yet unidentified, are agglomerates of vacancies in the form of small globules. There is a simple reason for the preference of interstitial-type extended defects to take disk shape: it is the geometry of minimum strain energy for a mismatched inclusion in a matrix, as shown by Nabarro (1940). An interstitial type inclusion represents an insertion of extra matter into a matrix and consequently produces a normal compression against the host matrix. A spherical cavity, by contrast, produces no. or very little. strain in the host matrix. It is for this reason that it cannot be detected by TEM (aside from a small change in matter density). For vacancy clusters. the spherical cavity is therefore the geometry of minimum energy, in both the strain energy and the surface energy components, and is the preferred form. A plausible explanation for the separate agglomeration of excess vacancies and self-interstitials among like species is that there may exist an energy barrier to the vacancy-interstitial recombination. One can see the rationale of the existence of a recombination barrier if one recognizes that the equilibrium configurations of the vacancy and the interstitial involve relaxation of atomic structure surrounding each defect (Hu. 1977a). From a study of the enhancedretarded transients of antimony diffusion under thermal oxidation. a recombination energy barrier of = I .4 eV has been estimated (Antoniadis and Moskowitz, 1982). As an alternative, an entropy barrier for vacancyinterstitial recombination has been proposed (Gosele, Frank, and Seeger, 1982). The idea derives from the suggestion (Seeger and Chik, 1968),that, at high temperatures, the silicon self-interstitial is an extended structure of a disordered region; and so, too, may be the vacancy. An extended point defect is one of the explanations for the very large preexponential factor experimentally found for the silicon self-diffusion. It is argued (Gosele et al., 1982) that the vacancy-interstitial recombination event is preceded by the reordering of the structures of both point defects that results in a negative entropy of about - I I .5 k. The vacancy-interstitial recombination will take place, regardless of which or both barriers: but the rate of recombination may not be fast enough to prevent self-agglomeration of vacancies and self-interstitials in parallel. De Kock and van de Wijgert

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(1980) have endorsed such a model for the formation of the A- and the B-defects. An alternative model (Petroff and de Kock, 1976; Fall, Gosele, and Kolbeson, 1977; Roksnoer, 1984) is that the self-interstitial is the predominant point defect in silicon at high temperatures, and that Bdefects are interstitial agglomerates that would collapse into A-defects. Two more types of microdefects, the C-defect (de Kock, Stacy, and van de Wijgert, 1979) and the D-defect (Roksnoer and van den Boom, 1981) have later been reported. The C-defect seen only sometimes, is somewhat of a mystery. The D-defect, like the B-defect, is very small and in general invisible to TEM. Nonetheless, Roksnoer and van den Boom suggested that it results from agglomeration of vacancies, a view that has received support from many subsequent investigators. However, a contrary view has been expressed by the Ioffe group (Sorokin et al., 1991), who reported that strain contrast of microdefects can be obtained with high-resolution electron microscopy and that all microdefects, including the D-defect, are of an interstitial type. Their model of microdefect formation is as follows: In regions of vacancy excess, vacancies will create complexes with interstitial oxygen atoms (not self-interstitials) to form D-defects. In regions of interstitial supersaturation, self-interstitials, oxygen, and carbon atoms agglomerate to form B-defects that, with further addition of self-interstitials, become A-defects. At present, a definitive conclusion about these microdefects remains unavailable. Under the experimental conditions of Roksnoer (1984), who grew his crystals by the pedestal method (somewhat similar to the floating-zone method), D-defects will not form until the crystal growth rate exceeds 5.4 mm/min. In contrast, A- and B-defects may start to form at a crystal growth rate of S0.2 mm/min, but will not form when the growth rate exceeds 4.5-5.0 mm/min. The threshold growth rates for the appearance and disappearance of various types of microdefects depend strongly on the diameter of the crystals and the method of crystal growth. For example, it has been reported that (Yamagishi et al., 1992), in their Czochralski crystals, D-defects start to appear at a growth rate of 5 0 . 8 mm/min. It should be noted that there are many differences between float-zone and Czochralski silicon crystals aside from the higher oxygen content in the latter. The temperature distribution during the growth is also quite different. While it would seem that the threshold growth rate may be indicative of the diffusion-limited annihilation velocity of a particular point defect species at the melt-crystal interface, model analysis is predicated on the appropriateness of assumptions. Voronkov (1982) has given estimates for C , , D,, C,, and D, from just such an analysis. But Voronkov’s formulation of the swirl defect formation is an oversimplification, considering the crystal velocity from the interface and the concentration gradient as the

5.

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IWIN I Ut~FECTSI N SILICON

159

only factors driving a point defect flux. Among the more important factors ignored is the thermal diffusion in a rapidly varying temperature field along the crystal axis. Also, the effect of impurity atoms on the formation of swirl defects. as has been noted by many researchers, was also not taken into account in Voronkov’s formulation. At the present time, there is still no satisfactory model for the formation of the various types of swirl defects, but they are undoubtedly manifestation of intrinsic point defects. There have been relatively few investigations of swirl defects in Czochralski silicon crystals. Most results (de Kock et al., 1979; de Kock and van de Wijgert, 1980; Pimentel and BritoFilho, 1983; Harada, Abe, and Chikawa, 1986; Yamagishi et al., 1992) seem to indicate similar behaviors in the formation of microdefects in both kinds of crystals. Hence. at the present time, it is difficult to assess the role of oxygen in the formation of microdefects. 111. Thermal Defects in Silicon

The subject of “thermal defects” in silicon has a rather interesting and protracted history. Since the first observation reported by Gallagher (1955), various investigators have reported that, when a silicon substrate is heated at some high temperatures (generally, 5800°C) for some length of time and then quenched, a significant concentration of deep-level donors is introduced into the substrate. These deep-level centers have since been called thermul defects. Early speculations on the identity of these centers range from silicon self-interstitials (Bemski and Dias, 1964) to vacancy clusters (Elstner and Kamprath, 1967; Boltaks and Budarina, 1969). In the investigation of Boltaks and Budarina (19691,the concentration of the thermal point defects was derived from measurements of the change in specimen density and lattice constant after quenching. Both Elstner and Kamprath (1967) and Boltaks and Budarina ( 1969) reported the energy of formation of “vacancy” to be 2.5-2.8 eV. Quenching experiments for the investigation of native point defects in silicon have proven to be difficult and unreliable. Unlike in most metals, the concentrations of both the self-interstitial and the vacancy are very low. The change in the length of a specimen is related to the change in the volume of the specimen by A l / l = AVC’I(3V). For an increase of the vacancy the length of a silicon specimen increases concentration by 1 x 10“ cm by less than 0.7 x lW7. a change too small to be measured accurately. Furt hermore. silicon samples can be easily contaminated by fast diffusing impurities such as copper, nickel, and iron, which can diffuse through silica furnace tube at high temperatures. While the opinions of various investigators diverged, their experimental results exhibit a high degree of

’,

160

s. M. nu

agreement. The donor level observed in various investigations was in a narrow neighborhood around ( E , + 0.40) eV. Various investigations since 1977 (Gerson, Cheng, and Corbett, 1977; Lee, Kleinhenz, and Corbett, 1977; Weber and Riotte, 1978; Feichtinger, Waltl, and Gschwandtner, 1978; Rijks, Bloem, and Giling, 1979; Weber and Riotte, 1980; Graff and Pieper, 1981; Glinchuk and Litovichenko, 1981), however, have led to the general consensus that the “thermal defects” are after all not native defects or their clusters but are contaminants from the furnace, passing through silica tubes, and getting into the silicon substrates. It may be remarked that Collins and Carlson (1957) already expressed their suspicion that there could be a connection between the thermal defects observed by Gallagher and the iron donor in silicon that they studied, because of their many similarities. IV. Self-Diffusion 1 . POINT DEFECTS AND SELF-DIFFUSION

Random movements of vacancies or self-interstitialcies give rise to self-diffusion: (1) DSC, = 4”D”CV 4- 4,D,CI, where D,, D,, and D, are the self-, vacancy, and interstitialcy diffusivities, and Cs, C,, and C , are the lattice site, vacancy, and interstitialcy concentrations, respectively. The terms 4v and 4, are the vacancy and the interstitialcy correlation factors, respectively, applicable to the diffusion of labeled lattice atoms occurring only in self-diffusion experiments. All other processes such as the Kirkendall effect, the shrinkage of stacking faults, the dynamic deformation-recovery , etc., involve the selfdiffusion of “normal” unlabeled host atoms for which the correlation factors are inapplicable and should be dropped from Eq. (I). As indicated in Eq. ( l ) , the self-diffusivity is a combination of the concentrationdiffusivity products of the vacancy and the self-interstitialcy. A possible contribution of Pandey’s (1986) concerted-exchange mechanism has not been included in Eq. (1). At the present time there is no experimental data in support of this model. In most materials, usually one species, either the self-interstitial or more often the vacancy, is overwhelmingly dominating and is the only species that needs to be considered for all practical purposes. It is one of nature’s fortuities that, in silicon, the vacancy and the self-interstitial are equally important, at least in the temperature range of practical interest. Two important properties of a point defect species are its concentration and diffusivity under intrinsic and equilibrium condition at a given temperature

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161

where the subscript X represents either I or V, SL and S; are the entropies of formation and migration, respectively, and H i and H," are the enthalpies of formation and migration. (Except in cases under high externally applied stress, we will use the internal energy, o r simply energy, in lieu of enthalpy.) Here, vo is the normal mode frequency, and r is the atomic jump distance. The asterisk denotes parameters under intrinsic (infinite dilution) equilibrium conditions. It follows that

Thus, the activation energy of self-diffusion Q is given by E.; + E," of whichever point defect species that dominates in a particular temperature range. 2 . SELF-DIFFUSION FROM ISOTOPEEXPERIMENTS Self-diffusion in silicon has been investigated experimentally over the years since the mid-1960s. The self-diffusion of silicon is very slow, so earlier experiments were usually carried out at temperatures 5 IIOWC. The activation energy of self-diffusion obtained from these experiments of varied methods falls in the rather narrow range of 4.8-5.1 eV (Peart, 1966: Masters and Fairfield, 1966; Mayer, Mehrer, and Maier, 1977). Later investigations extended to lower temperatures reported different activation energies. While Kalinowski and Seguin (1979) reported an activation energy of 4.7 e V in the temperature range 855-1175"C, Hirvonen and Antilla (1979) and Demond et al. (1983) reported activation of about 4.1-4.2 eV in the low-temperature range. Furthermore, Demond et al. (1983) also reported a break in the Arrhenius plot at about 1 100°C, with an activation energy of 4.9 eV in the high-temperature regime. A similar break in the Arrhenius plot for germanium diffusivity in silicon was reported by Hettich, Mehrer, and Maier (1979). There may be some similarity between germanium diffusion in silicon and silicon self-diffusion. The transition from the low-temperature to the high-temperature activation energy has been ascribed to a transition from a vacancy-dominated to an

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S. M . HU

interstitialcy-dominated diffusion, a concept first introduced by Seeger and Chik (Seeger and Chik, 1968; Frank et al., 1984). This implies Efy -k E P - 4 e V E; -k E r

- 5eV.

This set of hypothesized relations has in many cases served as constraints for the seeking to separate EG, E;, E;, and E," by model fitting of diffusion profiles. In order for the interstitialcy mechanism to operate at high temperatures, it is necessary that the sum of entropies for formation and migration be much larger for the self-interstitial than for the vacancy. It is not possible to deduce from these experiments of self-diffusion to identify the point defect that represents the dominant term on the righthand side of Eq. (1). Only experiments of self-diffusion carried out under controlled conditions of point defect supersaturations can help resolve this issue. While so far no such experiment of silicon self-diffusion has been carried out, an indication of nearly equal vacancy and interstitialcy contributions to silicon self-diffusion may be inferred from the investigation of Fahey, Iyer, and Scilla (1989b) on germanium diffusion in silicon under separate conditions of vacancy and interstitial supersaturations.

3 . SELF-DIFFUSION FROM KINETICS OF EXTENDED DEFECTS The activation energy and the self-diffusivity from these investigations based on direct measurement of the diffusion of silicon isotopes generally agree quite well with those inferred indirectly from defect kinetics that are controlled by self-diffusion. Some examples include the kinetics of shrinkage of dislocation loops (Sanders and Dobson, 1974), the annealing of preexisting oxidation stacking faults (Hashimoto et al., 1976; Sugita et al., 1977; Shimizu, Yoshinaka, and Sugita, 1978; Claeys, Declerck, and van Overstraeten, 1979; Lin et al., 1981; Nishi and Antoniadis, 1985; Rogers and Massoud, 1991b),and dynamic deformation-recovery (Brion, Schroter, and Seithoff, 1979). The activation energy of self-diffusion from most of the annealing studies of preexisting stacking faults are in the range 4.6-4.9 eV. In the somewhat lower temperatures range investigated by Sanders and Dobson (1974) (970-1070°C) and Nishi and Antoniadis (1985) (950-1O5O0C), an activation energy of 4.1-4.3 eV was obtained. The dynamic recovery gives an even smaller activation energy of 3.6 e V in the temperature range 850-1100°C (Brion et al., 1979). The author is not aware of any data available for self-diffusion at even lower temperatures. While the activation energy obtained from defect kinetics quite

5.

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163

POINT DI-FFCTS IN SILICON

accurately represents the activation energy of silicon self-diffusion, the preexponential factor of self-diffusion so obtained is much less reliable. This is because the kinetics of defect shrinkage comprises many unknown factors, and its formulation relies on many simplifying assumptions in modeling. The only parameter modeled reasonably accurately is the driving force behind the shrinkage of extended defects. C ', the concentration of self-interstitial in equilibrium with a stacking fault, is given by (Hu, 1981b)

c' = c*exp{&,[

"'

y t 2Trr( 1

-

u ) (In:

-

I)]].

(6)

In this expression, within the outer pair of brackets, the first term, y, is the faulting energy per unit area of the stacking fault, R is the atomic volume, and h is the magnitude of Burgers vector of the dislocation loop. The second term represents the strain energy due to the stacking fault. G is the shear modulus and w Poisson's ratio. For the extrinsic stacking fault in silicon, y is about 70 ergs cm (Alexander et al., 1980), or about 0.026 e V per atom. For perfect dislocation loops, such as in Sanders and Dobson's (1974) annealing experiments, y = 0 and drops out from Eq. (61, and the strain energy is the sole driving force for shrinking. For stacking faults that are sufficiently large, the strain energy term becomes negligible compared to the faulting energy, and Eq. (6) reduces to

~'

( 7 '

=

c"exp(2.j

for y>>

Gh' 2lTy(l - v ) '

(7)

Thus, this expression should be good for r 5 1 k m . The kinetic parameter, on the other hand, could be formulated as either reaction-diffusion controlled as given by Hu (1981b) or diffusion controlled as given by Giisele et al. (Gosele and Frank, 1981: Tan and Gosele, 1982). In inert ambients, and in absence of bulk sources of point defects such as oxygen precipitation, the formulation of Gosele et al. simplifies to

where a c t is + a geometrical factor for the diffusion-limited case, given by 2 n/ln(8r/rc),which is a weak function of r . The value of (D,CT + D , CT ) obtained from stacking fault shrinkage kinetics differ slightly from self-diffusion measured from isotope diffusion because of the absence of correlation factors here (q.v. Eq. ( I ) ) .

164

s. M. nu

V. Coexistence of Vacancies and Self-Interstitialsin Silicon By coexistence of the vacancy and the self-interstitial, we mean the comparable dominance and roles of these two point defects in silicon. This can now be regarded as a firmly established fact. The reasoning of the inevitability of this conclusion is based on the experimental observation of oxidation-enhanced diffusion, oxidation-retarded diffusion, and oxidation generation of extrinsic stacking faults. Between 1969 and 1971, several groups of investigators (Will, 1969; Bean and Gleim, 1969; Chan and Mai, 1970; Kovalev et al., 1970; Okamura, 1970; Katz, 1970; Allen and Anand, 1971; Higuchi, Maki, and Takano, 1971) reported an interesting phenomenon that, in oxidizing ambients, the diffusion rate varies with the crystallographic orientation of the silicon surface, in the order { 100) > (1 10) > (1 11). What was observed is actually the phenomenon of oxidation enhanced diffusion, an effect that varies with the surface orientation. The diffusion enhancement is greater in wet oxidation than in dry oxidation. A separate phenomenon had been reported several years earlier, that thermal oxidation of silicon often caused the formation of stacking faults (Thomas, 1963; Queisser and van Loon, 1964; Jaccodine and Drum, 1966; Booker and Tunstall, 1966; Fisher and Amick, 1966). The growth rate of OSF is also dependent on the crystallographic orientation of the surface being oxidized, in the order (100) > (1 10) > (1 1 I). The growth rate is higher for oxidation in wet oxygen than in dry oxygen. The similarities between the two phenomena, OED and OSF, led Hu (1974) to suggest that these two phenomena are closely related and have a common origin. Connecting OED to OSF brought us to the crucial point on our way to understanding diffusion in silicon. This is because the nature of the stacking fault can be determined from image contrast in transmission electron microscopy (Hirsch et al., 1965; Hashimoto, Howie, and Whelan, 1962). The OSF in silicon has been determined to be extrinsic in nature, namely, of the interstitial type (Jaccodine and Drum, 1966; Booker and Tunstall, 1966). The model of point defects and diffusion that Hu put forth on the basis of the connection between OED and OSF contains the following important elements (Hu, 1974): A. The vacancy and the self-interstitial coexist as major thermal point defects in silicon. The diffusion of group I11 and V atoms in silicon occurs via a dual mechanism mediated by both the vacancy and the self-interstitial. The ratio between the interstitialcy and the vacancy components varies according to the atomic species. B. Thermal oxidation of silicon injects excess silicon interstitials into the silicon substrate. The rate of injection is assumed to be directly

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proportional to the rate of thermal oxidation. The excess selfinterstitials are assumed to be annihilated at the surface, via a regrowth process that is dependent on the surface orientation and especially the density of surface kinks. C. Some of the self-interstitials in excess of the thermal equilibrium value would condense to form OSF, when nucleation sites are available. D. At the same time, the supersaturation of self-interstitials would enhance the diffusion of those substitutional dopants that exhibit an affinity with the self-interstitial. The difference in OED among various dopants then reflects the difference in the dopant‘s affinity with the self-interstitial. At that time, observations of OED were available only for boron, phosphorus, and arsenic; but the difference in OED among these was already sufficient to establish the dual mechanism as the only logical explanation possible. The interstitial nature of the OSF is indisputable from the TEM fringe contrast. But some early vacancy-only advocates had contended that, while they could accept that thermal oxidation generate silicon selfinterstitials, the existence of the self-interstitials as an important native point defect at thermal equilibrium had not been proven. One indication of the self-interstitial as an important thermal point defect came from Foll and Kolbesen’s (1975) identificaticin of type A “swirl defects” as being interstitial type dislocation loops that can come only from the agglomeration of silicon self-interstitials during crystal growth. There is another phenomenon of OSF growth that can allow only the conclusion that the OSF are interstitial disks. The phenomenon is associated with the precipitation of oxygen in silicon. When interstitially dissolved oxygen atoms agglomerate into an SiOz precipitate, a unit volume of silicon is converted to approximately 3.25 unit volumes of the precipitate. One way to reduce strain energy incurred by the localized volume expansion is to provide the needed cavity volume via the emission of self-interstitials or the absorption of lattice vacancies. Consequently there will be a supersaturation of self-interstitials or an undersaturation of vacancies. The supersaturation of self-interstitials due to oxygen precipitation have been shown by Hu (1980b) and Rogers et al. (Rogers et al., 1989: Rogers and Massoud, 1991a) to feed the growth of preexisting OSF. Most crucially, a one-point-detect theory cannot explain why the diffusion of different dopants would respond differently to a supersaturation of one point defect species: the diffusion of some dopants is enhanced more than others, while the diffusion of still other dopants is retarded. In the years that followed, a number of related phenomena have been discovered, all of which have greatly reinforced the dual vacancy-

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interstitialcy mechanism. These include the observation, by Mizuo and Higuchi (Mizuo and Higuchi, 1981), and Antoniadis and Moskowitz (Antoniadis and Moskowitz, 1982), of the oxidation retarded diffusion (ORD) of antimony, for which there is a very natural explanation: A supersaturation of self-interstitials causes an undersaturation of vacancies. If the antimony diffusion in silicon is mediated predominantly by the vacancy, it will be retarded during oxidation. There is also a physically intuitive interpretation for antimony’s preference for the vacancy mechanism. The elastic interaction between a point defect and a substitutional atom is dominated by the mismatch of the sizes of the lattice and the substitutional atoms. A larger substitutional atom is attracted to a vacancy while a smaller substitutional atom is attracted to a self-interstitial. A complementary phenomenon was subsequently discovered (Mizuo and Higuchi, 1982; Hayafuji, Kajiwara, and Usui, 1982; Fahey, Dutton, and Moslehi, 1983; Mizuo et al., 1983; Fahey et al., 1985), that thermal nitridation of silicon injects excess vacancies. That interpretation comes from the observations of OED-ORD of various dopants in thermal nitridation. The diffusion of phosphorus is retarded, while the diffusion of antimony is enhanced. This trend is just the opposite of that in thermal oxidation. With the observation of the complementary effect of nitridation, the logics of a dual-point-defect system is now seamless: OSF are interstitial in nature as identified by TEM fringe contrast, and corroborated by their growth during oxygen precipitation in inert ambients. Therefore, the formation of OSF indicates there is a supersaturation of self-interstitials or an undersaturation of vacancies during thermal oxidation. From the OED of boron and phosphorus and, to a lesser extent, arsenic, we conclude that these elements can diffuse via an interstitialcy mechanism. From the ORD of antimony, we must conclude that it diffuses via a vacancy mechanism. The fact that the antimony diffusion is enhanced by thermal nitridation must then indicate that nitridation generates excess vacancies. Finally, since the phosphorus diffusion becomes retarded in the presence of these excess vacancies, one can conlude only that, under normal conditions, it takes place predominantly through the vehicle of the selfinterstitial, whose concentration is reduced by annihilation with the excess vacancies during the nitridation.

VI. Interstitial Configurations and Charge-Enhanced Migration 1. GEOMETRICAL CONFIGURATIONS A N D MIGRATION PATHWAYS OF THE SELF-INTERSTITIAL

The generally accepted configuration of a lattice vacancy is simply a regular lattice site with a missing lattice atom. In contrast, conjectures

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n

F I G . I . The tetrahedral-interstitial configuration.

167

n

FIG. 2. The hexagonal-interstitial configuration.

for probable configurations of a n interstitial vary, with different claims of model calculations and experimental supports. The simplest conceptual picture of an interstitial is an atom sitting at a lattice interstice having the most ”open space” (in the hard-sphere model of the lattice atoms). In a diamond lattice, this interstice is the tetrahedral site (or the T site), with the four nearest neighboring atoms at the vertices of the tetrahedral (Fig. I). The interstitial atom can jump to any one of the four nearest tetrahedral sites by passing through a puckered hexagonal ring of atoms, of which three are at the vertices of a face of the tetrahedral. The center of this hexagonal ring, called the hr.urrgoncil sire (or the H site), is considered to be the saddle point (Fig. 2 ) . because the very little “open space.” The “hardness” of the spherical atoms (usually in terms of one of several forms of empirical interatomic potentials related to elastic properties) was used by a number of early researchers to determine the migration energy barrier of the interstitial. The larger is the interstitial atom, the larger would be the repulsive potential at the hexagonal site considered as the saddle point, and the larger would be the activation energy of migration. However, Weiser (1962) suggested that, for a small ionic interstitial, the tetrahedral site may not be the equilibrium site: it may instead be the saddle point. with the hexagonal site being the equilibrium site. He pointed out that an ion will cause a polarization of the lattice atoms surrounding it and that the magnitude of the polarization energy (which is negative) is larger for atoms closer to the ions. Therefore, one expects that the polarization would contribute a larger decrease to the energy of an ion at the hexagonal site than at the tetrahedral site. He calculated atomic polarizability from the macroscopic dielectric constant of silicon

168

s. M. HU

from Clausius-Mossotti’s relation, and obtained a polarization energy contribution of -4.67 eV for the tetrahedral configuration, and -5.43 eV for the hexagonal configuration. (A later, more accurate calculation by Hu and Weiser (Hu and Weiser, 1972; Hu, 1973) obtained -4.20 e V and -5.16 eV for the tetrahedral and the hexagonal site, respectively; but this would not materially affect the conclusion regarding an equilibrium site.) For small ionic interstitials, the repulsive overlap potential at the hexagonal site is small enough that it may be more than compensated for by the larger polarization energy at the hexagonal site. Weiser’s theory was motivated by the experimental observations that the activation energy of diffusion does not increase steadily with the radius of an ionic interstitial, as would be expected if the repulsive potential at the hexagonal site were the principal factor affecting the migration barrier. Weiser’s concept would afford an explanation of why the activation energies of diffusion are very small for some interstitial ions of intermediate size, e.g., copper. For such ions, the hexagonal and the tetrahedral sites may have nearly equal potential, resulting in very small migration barrier. It turns out, however, that this theory is not in accord with the experimental observations (Aggarwal et al., 1965; Watkins and Ham, 1970; Berry, 1970), which indicate lithium, a very small ion, to occupy the tetrahedral site in silicon. It was first pointed out by Seitz that the interstitial of the traditional view is not a counterpart of the vacancy. He proposed a configuration of an interstitial that would be a more logical counter part of the vacancy, and he called the interstitial of this configuration the interstitialcy (Seitz, 1950), now often called the split interstitial. Whereas the vacancy in a lattice is a lattice site with the lattice atom missing, the interstitialcy is a lattice site with an extra atom. There are some interesting characteristics that can be deduced for the interstitial of this configuration. Since an interstitialcy occupies a lattice site as does any host or substitutional atom, it is bound by the flux sum rule (Hu, 1992)

where subscripts A and B denote the impurity and the host atoms, and u ( t )is the velocity of the movement of the whole lattice relative to some stationary markers-the Kirkendall effect. When it moves from lattice site to lattice site, it exchanges positions with host lattice atoms as well as substitutional atoms, causing self- and impurity diffusion in a way that is analogous to a vacancy mechanism. A “regular” interstitial, on the other hand, will more likely migrate through the lattice all by itself, and the flux of this type of interstitial is not bound by the flux sum rule. It is

5.

n

FIG. 3. The hond-center-interstili~il configuration.

169

INTRIN5IC POINT Dt-FECTS IN SILICON

n

F I G . 4. The (100)-split-interstiIi~il configuration.

possible that a regular interstitial may displace a lattice atom when an interstitialcy saddle point energy i s lower than a “regular” (hexagonal or tetrahedral site) saddle point: but the flux of this interstitial is still not bound by the flux sum rule. A number of geometrical configurations of the interstitialcy can be conceived. Watkins ( 1966) speculated that a double-positive interstitial, with two dangling valence electrons, may bond with two lattice atoms in a bond-center configuration (or the B configuration) (Fig. 3 ) . Friedel (1967). on the other hand, proposed a (100)-split configuration (or the S configuration), as depicted in Fig. 4. From an internal friction investigation of boron-implanted silicon specimens, Tan, Berry, and Frank (1973) have speculated on a geometrical configuration of a ( 100)-split interstitial and a version of a (1 lO)-split interstitial (Fig. 3 ) . N o silicon self-interstitial has been identified by electron paramagnetic resonance (EPR) studies (although the EPR Si-G25 spectrum was tentatively identified as the isolated interstitial silicon (Watkins, 1975)). But Troxell and Watkins (1980) have reported a (100)-split configuration of a boron interstitial. Calculations based on the semi-empirical extended Hukel theory (EHT) (Watkins et al., 1971; Corbett. Bourgoin, and Weigel. 1973, Weigel et al., 1973), showed the (100)-split of Fig. 4 to be the lowest energy configuration for the neutral, single-positive, and single-negative charge states of the self-interstitial in both diamond and silicon. Next higher in energy was found to be the bond-centered configuration, then t h e hexagonal configuration, with the tetrahedral configuration being the highest. The finding that the tetrahedral site is the highest energy interstitial configuration of all charge slates is quite surprising. The reliability of the EHT calculations. however, has been criticized by Pantelides et al. (1983).

170

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M. HU

FIG.5. A (1 IO)-split-interstitial configuration.

On the other hand, from an angle-scanned channeling study of implanted boron in silicon, Swanson et al. (1981) concluded that about 40% of the implanted boron atoms are interstitial but are not located near tetrahedral or hexagonal interstitial sites. Rather, they have a bondcentered configuration. Nor can any of the interstitial boron aroms be characterized as having a (100)- or a (110)-split configuration. 2. CHARGE-ENHANCED AND ATHERMAL MIGRATION OF THE SELF-INTERSTITIAL Consider a neutral interstitial residing at a tetrahedral equilibrium site, with the hexagonal site being the saddle point. The potential energy at either site is decided largely by orbital overlap. If the interstitial atom now loses or captures an electron and becomes an ion, then, according to Weiser’s theory mentioned earlier, the energies at both sites will be lowered by an amount equal to the polarization energies for ions at the respective sites. The energy at the hexagonal site will be lowered by a larger amount (some calculated values are given in an earlier section). This is illustrated in Fig. 6 . It is possible that, if the energy of a neutral interstitial at the hexagonal site is only slightly larger than that at the tetrahedral site, the difference in polarization energy may tip the balance, making the hexagonal site the equilibrium site (Fig. 7), as proposed by Weiser for small ionic interstitials. Thus, after acquiring a charge, an interstitial at a tetrahedral site finds itself at an energy saddle point, with the neighboring hexagonal sites having become the equilibrium sites. It will then be able to move to a neighboring hexagonal site without thermal activation. It may subsequently capture an opposite charge and revert to

5.

INTHIN\I(

171

POIN1 DEFECTS IN SILICON

the neutral state, for which the hexagonal site is the saddle point. It can then move athermally to one of the neighboring tetrahedral sites. This is the uthermal migration mechanism proposed by Bourgoin and Corbett (1972). We should mention, however. that the tendency for an ion to prefer the hexagonal site as the equilibrium site is contrary to the results of first-principles calculation of Bar-Yam and Joannopoulos ( l984c), to be discussed in the last section. Their results show that the equilibrium sites for I " and I ' ' are the hexagonal and the tetrahedral sites, respectively . We have used the tetrahedral-hexagonal-tetrahedral transition as an illustration of an athermal migration mechanism because it is derivative of

H T H T H T FIG.6 . Charge-enhanced migration hy lowering of migration barrier energy. Solid curve: potential for a neutral intentitial: dashed curve: potential for an interstitial after capturing or losing an electron. 7 and H and the tetrahedr;rl and the hexagonal sites. respecficely.

..--..

,.--. .

. .

,.--..

. _ _ I

H T H T

. .

.---. . *.

*--.

H T

Pi(,. 7. The Bourgoin-Corbett mechanism of athermal migration: Ionization of an inter\titiid

fnr :in

c u w s the original \addle point t ( i hecome the equilibrium site. Solid curve: potential neutral interstitial: dashed curve potential for an interstitial after capturing or losing electron. r a n d H and the tetrahedral and the hexagonal sites. respectively. ii

172

s.

M.

nu

Weiser’s theory of ionic interstitials in silicon and because it is physically transparent. Other interstitial configurations such as the various splitinterstitials may also be capable of ionization-stimulated athermal migration. However, Frank, Seeger, and Gosele (1981) argued that athermal migration is not viable for the split configuration, because this configuration has no alternate location in a silicon lattice. Since they considered the split-configuration as the only likely self-interstitial configuration in silicon, they further suggested that the Bourgoin mechanism of athermal migration of the self-interstitial does not operate in silicon. Theoretical findings of the energies of point defects in various charge states and sites will be given in the last section. VII. Formation and Migration Parameters of Point Defects

There is a general acceptance of the activation energy of self-diffusion of between 4 and 5 eV, apparently because of the rather good agreement among results of very different experiments. However, there are very few direct ways to separate this activation energy into its component energies of defect formation and migration and the association of these energies with specific point defect species. The reliabilities of these few methods are also debatable. In the past decade, many investigators have attempted to obtain these parameters indirectly, by model-fittingdiffusion profiles of dopants and more particularly transition elements like gold and platinum. One cannot really say that any set of fitting parameters, including point defect formation and migration, that is uniquely suitable for one particular model represents the true physical parameters. Another attempted approach to determine defect (usually the self-interstitial) migration kinetics separately from its thermal formation is the study of flow of injected point defects from one surface across a silicon slice of varying thickness and measurement of its influence on the evolution of existing stacking faults or dopant profiles on the opposite surface.

I. STUDIES OF POINT DEFECTS FROM IRRADIATIONS In the section on thermal defects, we already mentioned the difficulty and failures of quenching from high temperatures in order to provide sufficiently high concentrations of point defects for study at low temperatures. In the early 1960s, EPR studies of silicon point defects were carried out, especially by Watkins (1965) and coworkers, at very low temperatures in silicon samples irradiated by MeV electrons. Thermally stimulated transient capacitance (TSCAP) and deep-level transient capacitance spectroscopy (DLTS) methods were introduced in the early 1970s (Sah et al., 1970; Lang, 1974). These techniques began to be used for the

5.

INTRINSIC POIN

r DEtFCTS IN SILICON

173

investigation of electron-irradiated silicon since the mid- 1970s (Brabant et al., 1976; Kimerling, 1977). Experimental investigations of radiationcreated point defects cannot produce such information as the enthalpies and entropies of formation. But they can yield such information as the activation energies of migration, the geometrical structure, and the electronic states of the point defects. One question that has not yet been resolved is whether the point defects created by energetic bombardment at low temperatures are the same point defects thermally created at high temperatures. And, assuming they are the same point defects, are their properties measured at low temperatures and in highly excited nonequilibrium states the same as at thermal equilibrium at high temperatures. It is expected that electron bombardment would create an equal number of vacancies and self-interstitials. It was somewhat of a mystery that, in low-temperature annealing of electron-irradiated silicon, only the vacancy and its various forms of complexes have been identified, the selfinterstitial and its various forms of complexes have not. In the case of aluminum-doped silicon, an explanation for the mystery came from the observation of aluminum interstitials (Watkins, 1965). In aluminumdoped silicon irradiated with I . S MeV electrons at 4.2 K , Watkins found a spectrum, Si-(318, that he identified as A l + ' . The production rate of these defects was high (-0.03 defect/cm', per electron/cm2)and similar to that of the isolated vacancies ( V and V - ) (Watkins, 1965). Watkins speculated that silicon interstitials produced by the irradiation had replaced substitutional aluminum atoms on lattice sites. The observation of boron interstitials has been interpreted in the same way (Watkins, 1975). All these processes were detected at 4.2 K when the self-interstitial must be mobile in order to produce these impurity interstitials. Such fast migration may be explained by the occurrence of the Bourgoin-Corbett mechanism of athermal migration mentioned in Section VI.2, as the system is highly excited under irradiation conditions. Another possibility is the absence or instability of states having odd number of electrons, making the interstitials invisible to EPR. Anderson (1975) has proposed a model to explain why defects in certain amorphous semiconductors are not paramagnetic, and hence undetectable by EPR. His explanation is that for deep-level defects within a semiconductor bandgap, the repulsive coulombic energy is more than offset by spin coupling and structural relaxation that may result from capturing (or expelling) a second electron at the defect. This property is now known as Anderson's negative-(/. Thus, I = (or I + ' ) may be a lower energy state than I - (or I + ) , and V' (or C ' ' + ) may be a lower energy state than V (or V' ). A question that has not been raised is: Have any extended interstitial defects, such as extrinsic stacking faults or the climbing of dislocations, +

174

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M. HU

ever been observed in Watkins's experiments? It may be noted that, while researchers using electron paramagnetic resonance see only vacancies in irradiated silicon, electron microscopists tend to see only interstitial-type ,stacking faults and dislocation loops, for example, in electron irradiated nickel (Makin, 1968; Makin, 1969). This is because each characterization technique has its own sensitivity limitations. The fast migration of the excess self-interstitials would likely allow them to agglomerate into interstitial-type dislocation loops. It is not clear, however, whether such loops have been observed (or examined) by Watkins and other researchers in their EPR studies. The silicon vacancy, while it could be frozen at 4.2 K, is also quite mobile at cryogenic temperatures, with migration energies of -0.33 and -0.18 eV in the neutral and doubly negative charge states, respectively (Watkins, 1965; Watkins, 1968). The migration energy of 0.33 eV was later revised to 0.32 eV (Watkins, Troxell, and Chatterjee, 1979). A defect that anneals out with an activation energy of 0.45 eV has not been firmly established, but is thought to be that of the doubly positive vacancy (Watkins et al., 1979). The vacancy charge states show an Anderson negative-U property and the levels are assigned as follows (Watkins and Troxell, 1980; Newton et al., 1983): 1. 2. 3. 4.

Vacancy Vacancy Vacancy Vacancy

donor level at E , + donor level at E , + acceptor level at E , acceptor level at E ,

0.05 eV for V o+ V + + e-. 0.13 eV for V + + V + + + e-. - 0.57 eV for Vo + e- + V - . - 0.11 eV for V - + e- + V = .

Because of the negative-U properties of the vacancy charge states, the V - species, mentioned earlier with a migration energy of 0.33 eV, is supposed to be unstable and does not exist normally. It can, however, be brought into existence in, for example, a photo-excited system, in which electrons from V = can be pumped into the conduction band. The charge state of a point defect is important because it affects not only the mobility of the defect, but also its thermal equilibrium concentration, which, of course, also depends on the Fermi level as shown by Shockley et al. (Shockley and Last, 1957; Shockley and Moll, 1960). For example, for defect Ex- having two acceptor states, the concentrations of its singly negative and doubly negative states are

5.

INTRINSIC POIN I DEE t C I S IN SILICON

175

Doubly negatively charged defects, assumed to be vacancies, have been found to be necessary for a satisfactory simulation of arsenic diffusion profiles by Chiu and Ghosh (1971). The equilibrium concentrations of Eqs. (10) and ( I I ) are based simply on statistical thermodynamics; according to the tenet of energy balance, the formation energy of the ionized defect is the same as that of the neutral defect plus the difference between the Fermi level and the defect state energy. Some theoretically calculated results of the formation energies of variously charged defects (Section VIII) appear to contradict this tenet. 2. VACANCY FORMATION ENERGY FROM POSITRON-LIFETIME MEASUREMENTS It has long been postulated that lattice vacancies, which represent localized volumes without positive nuclear charge, tend to trap positrons, thus delaying their annihilation with electrons. The lifetime of positrons trapped by lattice vacancies affords an estimate of the concentration of vacancies. Based on positron-lifetime experiments conducted in the temperature range between 300 and 1523 K . Dannefaer, Mascher, and Kerr (19861, reported an enthalpy of formation of 3.6 ? 0.2 e V , and an entropy of formation of 6 to 10 k. These values seem reasonable in view of other types of experimental results. However, many assumptions which are made in the analysis of such measurements, may influence the reliability of results . 3 . POINT DEFECT CONCENTRATIONS FROM

‘rHERMAL

EXPANSION

MEASUREMENTS At higher temperatures, more point defects are incorporated into a crystal and, depending on whether the dominant point defect is the vacancy or the self-interstitial, will cause the volume of the crystal to expand or contract by an amount that is in addition to the normal thermal expansion of the lattice. However. as we already mentioned in Section 111, the incorporation of “thermal point defects,” which are actually fastdiffusing metallic contaminants, will also expand the volume of a given crystal. There is a discrepancy between the thermal expansion coefficient from length measurements of Okaji (1988) and the thermal expansion coefficient from lattice parameter measurements of Okada and Tokumaru (1984). Okada (1989) assumed that the larger thermal expansion from length measurement is a direct result of a larger ( C , - C , ) and gave a value of I .8 x 10’6cm-3at 1300 K for (C,, - C , ) . However, some important points of his results are open to question. First, from the same figure (his Fig. I ; Okada, 1989) from which he drew the preceding conclu-

176

s.

M. HU

sion, one would obtain ( C , - C , ) of about the same value at 1073 K as at 1300 K, as if the formation enthalpy of the majority defect were essentially zero. The data and interpretation are even more problematic at lower temperatures: From 500 to 700 K, C v - C , (again from Okada's Fig. 1) would now become negative, but its magnitude on the order of 1016cm-3is still about the same as at 1300 K. Granted that a negative value may simply indicate that the self-interstitial is the predominant point defect at low temperatures. But we should also expect the concentrations of both the vacancies and the self-interstitials in silicon at 300500 K to be immeasurably low, not the same magnitude as at 1300 K according to Fig. 1 of Okada (1989).

4. ESTIMATION OF SELF-INTERSTITIAL CONCENTRATION FROM OXYGEN PRECIPITATION Oxygen at the level of = 10'8cm-3 dissolved interstitially in cruciblegrown silicon crystals will usually precipitate out as SiO, in thermal processings at temperatures lower than the silicon melting point (1410°C). The volume of an SiO, precipitate is about 2.25 times the volume of the silicon consumed locally by the precipitate. Thus, a precipitated SiO, inclusion gives rise to an immense local stress, which may be relieved in a number of ways (Hu, 1986a). At high temperatures, it is feasible and efficient for the stress to be relieved by emission of silicon self-interstitials (Hu, 1986a). The evolution of excess interstitials during oxygen precipitation have been found to affect the growth and shrinkage of preexisting stacking faults (Hu, 1980b; Rogers et al., 1989; Rogers and Massoud, 1991a). At high temperatures, for example, FI100°C, the oxygen precipitates take the form of octahedron, which is the geometry of minimum surface energy, but is also the geometry of maximum misfit strain energy. Yet, in TEM lattice images, the regions of the silicon lattice surrounding such octahedral SiO, precipitates are completely free of strain. The existence of a significant lattice strain would be incompatible with the octahedral precipitate morphology, and would have caused the SiO, precipitate to prefer a platelet morphology, thereby trading a smaller surface energy for a smaller strain energy (Hu, 1986b). The absence of any strain around octahedral precipitates can be interpreted only as due to the emission of self-interstitials at a rate of 0.58 interstitial per oxygen atom precipitated. Because the rate of the disappearance of interstitially dissolved oxygen can be accurately measured by means of infrared spectroscopy, the rate of bulk generation of self-interstitials can also be determined quite accurately (this is quite unlike the case of the generation of self-interstitials by the thermal oxidation of a silicon surface). Hu (1980b; 1981a) has

5.

177

INTRINSIC POINT DEFFCTS IN SILICON

12 10

3-. $

8

+-

z

2

6

i

u-

4

V-

v

2 0

0

10

20

30

40

so

Time, hours Fit,. 8 The evolution of cxceb\ wlt-inter$titial in a bilicon sample containing oxygen and annealed at I?O(K’.

found that the interstitial oxygen decays exponentially. By relating this precipitation kinetics to the kinetics of the growth and shrinkage of stacking faults, he was able to derive an analytical expression for the evolution of excess self-interstitials during oxygen precipitation. (A numerical solution may be required if the precipitation kinetics is more complex.) An example of the results of his analysis of the evolution of excess selfinterstitial at 1200°C is shown in Fig. 8. He also obtained the equilibrium concentration of self-interstitials through the following relationship (Hu, 1992):

5 . DIFFUSIVITY OF THE SEL.F-~NTERSTITIAL FROM MEMBRANE EXPERIMENTS

Several investigations have been made using a “membrane” method (Taniguchi, Antoniadis, and Matsushita, 1983; Taniguchi and Antoniadis, 1985; Griffin et al., 1985; Scheid and Chenevier, 1986; Ahn et al., 1987; Griffin et al., 1987; Rogers and Massoud. 1991b). In this method, silicon “membranes” of different thickness. tens to hundreds of km, are prepared. lnterstitials are injected from the back side of a specimen by thermal oxidation. while the front side is protected from oxidation by a nitride or nitride-oxide composite film. The injected interstitials will flow through the thickness of the membrane to the front side and get annihilated there. By measuring the evolution of preexisting stacking faults or

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s. M. HU

dopant profiles on the front side, the self-diffusivity can be obtained through appropriate modeling. The complications come from the frontside interface reactions, and the bulk trapping of the excess interstitials. The bulk recombination has been neglected in most analyses. As demonstrated by Griffin et al. (1987), the enhanced diffusion on the frontside differs between specimens from float-zone and Czochralski silicon crystals, with the enhancement reduced in the Czochralski specimen. ~ ) Since Czochralski silicon contains a high concentration (= 10l8~ m - of oxygen atoms, it may be concluded oxygen could act as traps for the injected interstitials. However, Rogers and Massoud (Rogers and Massoud, 1991b) reported no difference between float-zone and Czochralski silicon substrate in bulk trapping of self-interstitials migrating across the thickness of silicon wafers. The bulk generation-recombination of Frenkel pairs have also been neglected in these studies. The results obtained from these studies vary widely. 6. DEFECT PARAMETERS FROM MODEL-FITTING Au

AND

PT DIFFUSION

Gold diffusion in silicon was traditionally analyzed in the FrankTurnbull dissociative mechanism (Frank and Turnbull, 1956). In this model, the gold atoms diffuse interstitially very rapidly through the specimen and become saturated. Because gold has a larger substitutional solubility than interstitial solubility, further diffusion of gold will continue through the following reaction:

Aui

+ V*

Au,.

(13)

Gosele, Frank, and Seeger (1980) proposed an alternative mechanism through the following reaction Aui + Si,i+Au,

+ I.

(14)

In this mechanism, an interstitial gold atom takes up a substitutional site by “kicking out” a silicon lattice atom, Si,. This mechanism is now often referred to as the kick-out mechanism. (We may note that replacement is perhaps a more appropriate term, since it also states unambiguously the fact that this is a replacement reaction-a silicon lattice atom is replaced by a gold atom. The term kick-out does not simultaneously suggest that the gold atom takes up the position left by the kicked-out silicon atom. Kick-out will more appropriately denote the ejection of a lattice atom by an energetic agent, e.g., high-energy electrons or ions, photons, or electron-hole reaction events.) If both the vacancy and the selfinterstitial concentrations are maintained near their equilibrium value, due to the very large diffusivities of these two point defects, then there

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INTRINSIC POIN I DEFtCTS I N SILICON

179

is really no difference between these two mechanisms. However, if the diffusion of these point defects from or to the surfaces of the specimens cannot keep u p with the preceding two reactions, a difference arises not only in the point defect concentration profiles, but also in the gold concentration profiles, as shown by Cosele (1980) in an approximate analysis. They contended that the gold profiles from the kick-out model exhibit a U-shaped distribution, in agreement with experimental finding. This model has since been utilized by a number of investigators (Morehead et al., 1983; Morehead. 1988; Coffa et al., 1988; Boit, Lau, and Sittig, 1990; Zimmermann and Ryssel, 1992a; Zimmermann and Ryssel, 199%; Mathiot, 1992) to obtain the silicon self-diffusivity and even the diffusivity of the self-interstitial. Zimmermann and Ryssel (1992a; 1992b) have considered both the dissociative and the replacement mechanisms, as well as the bulk recombination between vacancies and self-interstitials in their analysis. Their results for the temperature range 700-950°C are summarized in the following:

CF

=

1.94 x lO”exp(

DI= 2.58

x 10

-

3.835 eV/kT)

’ exp( -0.965 eV/kT)cm’/s,

Ct

=

1.83 x IO”exp(- 1 . 1 6 2 e V / k T ) ~ m - ~ ,

D,

=

1.09 x lo3exp( - 2.838 eV/kT) cm’/s.

(15)

The vacancy formation enthalpy given by Eq. (IS) seems to be unreasonably small. Furthermore, according to Eq. (2). a preexponential factor of 1.83 x lof9for Ctr would imply a negative formation entropy, something that is not possible. Assuming that only the kick-out mechanism operates, and ignoring vacancy-self-interstitial generation-recombination, Boit et al. (Boit et al., 1990) have obtained from rapid optical unneufing of gold diffusion in silicon the following results:

D, = 1.03 x IOhexp(- 3.22 eV/kT) cm’/s, (16)

CF = 3. I 1 x 10”exp ( - I .58 eV/kT) cm-3.

VIII. Defect Energetics and Pathways from Theoretical Calculations

Theoretical calculations of the energies of formation and migration of the vacancy and the self-interstitial in silicon were made in the 1960s by use of empirical pairwise interatomic potentials (Swalin, 1961; Scholz and Seeger, 1963; Hasiguti. 1966). In the last several years, several new empirical interatomic potentials have been introduced for attempting better descriptions of covalent materials with some ad hoc terms to account

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S. M. HU

for environments beyond pairwise interactions. Such empirical interatomic potentials have been employed in a number of recent investigations for the calculations of the energetics of the vacancy and the selfinterstitial in silicon (Batra, Abraham, and Ciraci, 1987; Baskes, Nelson, and Wright, 1989; Ungar et al., 1993; Maroudas and Brown, 1993). Reasonable results, though not agreeing with each other, have been reported in all these investigations. But faith in such calculations would seem unwarranted, in view of the lack of theoretical basis in such empirical potentials. All scientists know that empirical formulas cannot be stretched too far. While some such empirical potentials are acceptable for calculating energies resulting from small changes from equilibrium lattice parameters, they cannot be expected to produce reliable predictions for drastic changes involving rearrangements of valence electrons in the formation of point defects. In particular, empirical interatomic potentials cannot provide means for calculating the energetics of point defects in their different charge states, which can be quite complex and unexpected (e.g., the occurrence of “negative-U” system mentioned in Section V1I.I). In the early 1970s, it is quite popular to calculate the energetics of point defects by use of semi-empirical extended Hiickel theory. Some of such calculations were mentioned in Section V1.I. The reliability of the EHT method has been criticized by Pantelides et al. (1983). Since the late 1970s, the energetics of the silicon vacancy and the self-interstitial have been obtained with first-principle calculations of total energy of a crystal containing a defect. In these calculations, the total energies of a perfect crystal and crystals containing a point defect at different lattice locations are calculated, and the appropriate differences then give the formation energy and migration energies along different paths. The Schrodinger equation is solved for a crystal containing a defect for a self-consistent pseudopotential (including the exchange-correlation energy). The self-consistency in the pseudopotential is achieved, by iterative computations, using the density-functional theory in the local density approximation for calculating the exchange-correlation potential (Kohn and Sham, 1965). These calculations are accomplished via two schemes: the use of self-consistent Green’s function method for a finite defect cluster (Baraff and Schluter, 1978; Bernholc, Lipari, and Pantelides, 1978; Lipari, Bernholc, and Pantelides, 1979; Bernholc, Lipari, and Pantelides, 1980; Baraff, Kane, and Schiilter, 1980; Caret al., 1984, Baraff and Schliiter, 1984; Car et al., 1985; Kelly and Car, 1992), and the method of supercell that contains 16 or 32 nearest atoms surrounding a defect and replicates by translations (Bar-Yam and Joannopoulos, 1984c; Bar-Yam and Joannopoulos, 1984b; Bar-Yam and Joannopoulos, 1984a;

5.

181

INTRINSIC POINT DEFECTS I N SILICON

Antonelli and Bernholc, 1989; Nichols, Van de Walle, and Pantelides, 1989). Up to 64 atoms are included in a supercell in a recent calculation (Sugino and Ashiyama, 1992)for the migration of impurity atoms, which would have to move away from the point defect to at least the third coordination site in order to return to the point defect at the nearest neighboring site that is different from the originating site. And it is also necessary to avoid the possibility of a percolation phenomenon (Mathiot and Pfister, 1982) in which [he point defect migration is short-circuited through closely spaced impurity atoms. The limitation on the reliability of these calculations is at present handicapped by the size of the supercell, or cluster, used, due to the limitation of present-day computer power. Thus, one problem with such calculations is that elastic relaxation and, particularly, electrostatic potentials are long range, occurring over many atomic shells. The effect is particularly evident in Weiser's (1962) calculations of polarization energy due to an interstitial ion. A typical supercell scheme would force these long-range effects to terminate at the third or the fourth coordination site, with unknown consequential errors. Bar-Yam and Joannopoulos ( 1984~)obtained from their calculations that equilibrium sites for I" and I ' are the hexagonal and the tetrahedral sites, respectively. This is just opposite to what one would expect from the effect of ionic polarization according to Weiser theory, as discussed earlier. The migration energies they calculated, with lattice relaxation, are I .O and 1.4 eV for I" and 1 ' , respectively. They later revised their results (Bar-Yam and Joannopoulos. 1984a) to 1.2 eV for the selfinterstitial in either charge state. They further differentiated the equilibrium geometrical figurations between p-type and n-type silicon, and reported that (Bar-Yam and Joannopoulos, 1984a), in n-type silicon. the tetrahedral site is the equilibrium site for I and the hexagonal site is the saddle point-i.e., the reverse of the p-type situation. Again, the hexagonal-tetrahedral configuration is the reverse for I" between p-type and n-type silicon. This finding is interesting, but does not seem to have an easy physical explanation. What differentiates n-type and p-type silicon is electrons in the conduction band that are not localized and are not originated from the neighborhood of the point defect. As such, why should they so strongly affect the potential energy at different sites'? One would intuitively suppose that the doping type, in terms of the Fermi level, would merely shift the formation energy of a charged defect uniformly in real space. In n-type silicon, the concentration of I would be low according to Fermi statistics as shown by Shockley et al. (Shockley and Last, 1957; Shockley and Moll, 1960). Bar-Yam and Joannopoulos (1984a) did not discuss this problem in their paper. Car et al. (1984) have also calculated the silicon self-interstitial energet+

+

+

+

+

+

182

S.

M. HU

ics for various geometrical configurations and charge states. They found that the tetrahedral site is the equilibrium site for Z , with the hexagonal site being its saddle point. This tetrahedral-hexagonal geometrical configuration is reversed for Zo, which is again in disagreement with the polarization energy concept of Weiser. Another peculiarity in the totalenergy vs geometrical location plot for Zo from the results of Car et al. (1984) is the existence of an energy cusp at the tetrahedral site. In the results of Car et al., the effect of the Fermi level is simply to shift the formation energy uniformly in real space by an amount equal to the Fermi energy (or twice that amount for doubly charged defects), up or down according to the sign of the charge. This is physically expected. They calculated the total energies for I + + , I + , and Zo. Their results suggest that the Bourgoin-Corbett mechanism may occur along the TB path: An I + + at the tetrahedral site (T) captures an electron and becomes I + , which then finds the neighboring bond-center site (B) to be at a lower energy and moves there without thermal assistance. Another possible path for the Bourgoin-Corbett mechanism was suggested to be the TBTH path. The BS path (bond-center to split-interstitial) of athermal migration, proposed earlier by Watkins et al., (1971), was found not to be possible. They found that I + is not a table charge state. In other words, Zo, I + , and Z + + form an Anderson negative-U system. Bar-Yam and Joannopoulos (1984~;1984b; 1984a), Car et al. (1984; 1985), and Kelly and Car (1992) did not report any negatively charged self-interstitials. This appears to be in conflict with the experimental evidence that phosphorus diffuses in silicon via a dominantly interstitialcy mechanism (Strunk, Gosele, and Kolbesen, 1979; Fahey, Dutton, and Hu, 1984; Nishi and Antoniadis, 1984; Fahey et al., 1989a), and that phosphorus diffusion is enhanced by electron concentration, almost to the second power (for example, see Fair, 1981; Fahey et al., 1989a), indicating that the self-interstitial may have a dominant double-negative charge state. (The concentration of neutral defects is independent of the Fermi level (Shockley and Last, 1957, Shockley and Moll, 1960).) The values of EC, Ei7, E;, and Ej" vary somewhat from different calculations. A summary of the results from various theoretical calculations is given in Table 1. The pressure dependence of defect energetics in silicon appropriate for self-diffusion, including the concerted-exchange mechanism of Pande y (1986), has been calculated by Antonelli and Bernholc (1989). The pressure dependence of defect energetics in silicon appropriate for impurity diffusion has been calculated by Sugino and Ashiyama (1992). They found that the activation energies for the diffusion of phosphorus, arsenic, and +

+

5.

183

INTRINSIC POINT DEFECTS I N SILICON

TABLE I

THEORETIC A1 F O R M A T I O N A N D MIGRATION ENERGIES (ev) OF INTRINSIC POINTDEFFCTS I N SILICON. ~~

E : or E :

Defect

I*'cT)

l"(T)

4.7 i- 0.5 4.0 3.6 4.4 4.3

~~~

~

E;"

Or

F"' -I'

References

0.4

2

0.2

2

0.5 0.2

2

0.5

Baraff and Schluter. 1984 Bar-Yam and Joannopoulos. 1984b Antonelli and Bernholc, 1989 Kelly and Car, 1992 Baraff and Schluter. 1984 Bar-Yam and Joannopoulos. 1984h Antonelli and Bernholc. 1989 Kelly and Car. 1992 Antonelli and Bernholc, 1989 Antonelli and Bernholc, 1989 Kelly and Car, 1992

I. 2

1.6

1.2 i- 0.3

4.3

0.3 I" ( € 3 ) \'I1

5.0 4.4 4.4 (unrelaxed)

antimony in silicon decrease with pressure for the vacancy mechanism, but increase with pressure for the interstitialcy mechanism. Taken together the experimental results of Nygren et al. (1985), which showed the diffusion of arsenic in silicon to increase with pressure, they (Sugino and Ashiyama, 1992)concluded that arsenic diffuses in silicon via a dominantly vacancy mechanism. However, they seemed to have neglected the fact that what Nygren et al. measured is the pressure effect on the activation enthalpy, rather than the activation energy, of diffusion. Sugino and Ashiyama (1992) reported a decrease of activation energy of diffusion by 0.6 eV at 60 kbar. Taking this value, the activation enthalpy, which includes a term of P A V of about 0.68 eV ( A V being approximately given by the atomic volume), would be +0.08 eV. A similar correction (but with an opposite sign) is needed for the activation enthalpy of the diffusion via an interstitialcy mechanism. In view of the accuracy of such supercell calculations, a definitive assessment of the diffusion mechanism is not warranted. While total energy calculations based on the local-density approximation have yielded remarkably good results, insofar as their compatibility with experimental data of self-diffusion is concerned, some of the limitations and reliability of such calculations should be noted. Kelly and Car (1992) have noted that for the calculation of the formation energy of silicon, a relaxation of the next-nearest neighbors would give such a huge change in value that a reliable first-principles calculation with a sufficiently large cluster is impractical for present-day computers. A similar

184

s. M. nu

problem occurs in the supercell method. A practical limit on the size of the supercell leads to very large dispersion in the gap state. Furthmiiller and Fahnle (1992) have noted that, for chalcogen defects in silicon, a significant dispersion occurs even for a supercell size of 128 atoms. Furthermore, the density-functional theory is a theory for the ground state. In the local-density approximation, it has proven unreliable for energies of excited states, such as the conduction band and conduction-band derived states. This caveat has indeed been noted by some authors of those calculations, of whom some would refrain from giving values for such energy states. However, the calculations of the total energy in terms of atomic arrangement have given some surprising good results, in view of the agreement reported among various research groups, as well as with experimental results.

IX. Summary In addition to their well-known roles on atomic diffusion and the formation and the dynamics of extended crystalline defects, vacancies and self-interstitials also affect the nucleation and precipitation of oxygen in silicon (Hu, 1977b; Hu, 1980a; Schaake et al., 1981; Craven, 1981; Oehrlein et al., 1982; Tan and Kung, 1986; Shimura, 1992). Conversely, oxygen precipitation causes excess self-interstitials and depletes vacancies, thereby affecting diffusion and defect processes (Hu, 1980b; Rogers et al., 1989; Kennel and Plummer, 1990; Rogers and Massoud, 1991a). With appropriate modeling, the kinetics of oxygen precipitation can provide an estimate of not only the supersaturation of silicon self-interstitials, but also their thermal equilibrium concentration (Hu, 1980b; Hu, 1992). Evidence from a wide variety of experimental observations indicates that both the vacancy and the self-interstitial coexist in silicon in almost equal roles. They have comparable energies of formation and of migration. They all contribute to the self-diffusion and the diffusion of substitutional impurities in silicon; but their relative roles vary for different impurities. The silicon self-interstitial has a number of different configurations, and moves through the lattice via different migration paths. Firstprinciples total-energy calculations, using local-density approximation to achieve self-consistency in defect potential, have given some surprisingly good results that are compatible with experiments. But there are some limitations and the question of reliability of such calculations. Possible errors, some quite large, arise from two main causes: (1) the size of clusters or supercells, sufficiently large to avoid the convergence and dispersion problems, cannot be handled by modern computers; (2) the inherent problem of the inability of the local-density approximation to

5.

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185

handle excited states. A rather unique feature of point defects in silicon, both the vacancy and the self-interstitial, is that the formation energy is very large. about 4 eV or more, and the migration energy is very small, about I eV or less. In spite of the probable errors, reasonably good values of the energy of formation and migration have been produced by theoretical calculations. On the other hand, attempts to produce separate values of formation and migration enthalpies by model-fitting experimental diffusion data, as well as other experimental approaches, e.g., diffusion of excess point defects through membranes, cannot at present be regarded as so successful.

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Sanders. I . R . . and Dobson. P. S. (1974). 1. Muter. Sci. 9, 1987. Schaake. H . F.. Barber, S. C., and PiniLzotto, R . F. (1981). In SL.miconduc/o,.Silicon 19x1, H. R . Huff. R. J . Kriegler. and Y . Takeishi (eds.). p. 344. Electrochemical Society. Pennington. N . J . Scheid. E.. and Chenevier. P. (1986). P17v.s. S r e r r . Solidi A 93, 523. Scholr, A . , and Seeger, A. (1963). Pliv.\. S t o r . Solidi 3, 1480. S t e r r i t s Solidi 29, 455. Seeger. A.. and Chik. K. P. (1968) t'lrr.~. Seitr. F . (1950). Actti Cryst. 3, 355. Shiniim. H.. Yoshinaka. A.. and Sugitir. Y . (1978). Jpn. J . A p p l . Phys. 17, 767. Shimura. F. (1992).J . Appl. P l r y s . 72, 1642. Shiniura. F..Dywn, W.. Moody. J . W., and Hockett. R. S . (1985). In V L S l Science und 7 6 . c k n o l o g y i l Y X 5 . W. M. Bulli\ and S. Broydo (eds.),pp. 507-516. Electrochem. Soc., Pennington. N.J. Shockley, W.. and Last. J. T. (1957). P h y s . Re\,. 107, 392. Shocklry. W.. and Moll. J . L. (196tl). Plrvs. Rei,. 119, 1480. Sorokin. L. M.. Sitnikova. A . A , . C'hervonyi. 1. F.. and Fal'kevich. E . S . 11991). Soi,. P/iv.\. Solid Sttrtr 33, 1824. Struck. H.. Gosele. U., and Kolbe\en. 13. 0. (1979). Appl. Phvs. Lett. 34, 530. Supino. 0.. and Ashiyama. A. (1992). P/rv.\. R ~ L B, . 46, 12335. Sugita. Y . . Shiniiru. H.. Yoshinaka. A . . and Aoshima. T. (1977). J . Vuc. Sci. Tec+~nol.14, 44.

Swalin. K. A . (1961). J . P h y s . Chrvti. S ~ l i d18, ~ 290. Swanwn. M . LA.. Howe. L . M., Saris. F. W.. and Quenneville. A. F. (1981). In Dyft,u.s in .S[,tt7ic,[,ndrrc,tor.\. J . Narayan and T. Y. Tan leds.). p. 71. North-Holland, New York. l'an. S . I . . Berry. B . S . . and Frank. W. i 1973). I n Ion Implantation in Srmiconducrors und Other Muteriirls. B. L . Crowdet (ed.), p. 17. Plenum Press. New York. l'an. T. Y . . and Cibsele. C . (1982).J . Appl. Phy.s. 53, 4767. Tan. T. Y . . and Kung. C . Y . (1980). In Setnic.ondrccior Silicon lYB6. H. R . Huff. T. Abe. and B. Kolbesen (eds.). p. 864. Electrochemical Society. Pennington. N.J. Taniguchi. K.. and Antoniadis. D. A . (1985). A p p l . Phys. Lett. 46, 944. Taniguchi. K.. Antoniadis. D. A. and Matsushita. Y . (1983). A p p l . Phvs. Lert. 42, 961. Thomas. D. J . D. (1963). Phvs. S t c r t . S,~lidi3, 2261. Troxell. J . R . . and Watkins. G . D. ( 19x0). P h y s . Re\,. B 22, 921. Tsuya. H . . Kondo. Y . . and Kananiori. M. (1983). Jpn. J . Appl. Phvs. 22, L16. Ungar. P. J . . Takai, T.. Halicioglu. 'I.. and Tiller, W. A. (1993). 1. Vuc. Sc,i. Techno/. A 11. 1-24.

Voronkov. V . V. (1981). J . Cpsr. G r o w t l r 59. 625. Wada. K . (1984). Phv.). Rci.. 30, 5x84. Wada. K . , and Inoue. N . (1986).In .Sc,nric.ondr~c.torSilicon lYX6. H. R. Huff, T. Abe, and B. Kolbesen (eds.), p. 778. Electrochemical Society. Pennington, N.J. Watkins. G . D. ( 1965). Rudiurion /)trrrrtiyr irr Sc,nric,ondr~ctors.p. 97. Dunod. Paris. Watkins. G . D. (1966). Quoted by ('orheit et al. (1973). Watkins, G . D. (1968). In Ruditrriori Dunicrgr iti .Srmic.onductors, F. L. Vook (ed.), p. 67. Plenum Press, New York. Watkins. G . D. ( 1975). In Ltittic.e I)t.fi.c I \ in Srniic,ondrrc,tor.s lY74. F. A . Huntly (ed.),p. 23. Institute of Physics, London Watkins. G . D.. and Ham. F. S. (1970). Pliys. Rev. B 1, 4071. Watkinh. G . D.. Mes5mer. K. P.. Weigel. C . , Peak. D.. and Corbett. J . W. (1971). Phvs. Re\.. L e t t . 27, 1573.

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Watkins, G. D., and Troxell, J. R. (1980). Phys. Rev.Lett. 44, 593. Watkins, G . D., Troxell, J. R., and Chatterjee, A. P. (1979). In Defects and Radiation ESferts in Semiconductors 1978, J. H. Albany (ed.), p. 16. Inst. Phys., Bristol. Weber, E., and Riotte, H. G. (1978). Appl. Phys. Lett. 33, 433. Weber, E., and Riotte, H. G. (1980). J . Appl. Phys. 51, 1484. Weigel, C., Peak, D., Corbett, J. W., Watkins, G. D., and Messmer, R. P. (1973). Phys. Rev. B 8, 2906. Weiser, K. (1962). Phys. Rev. 126, 1427. Will, G. N . (1969). Solid State Electron. 12, 133. Yamagishi, H., Fusegawa, I., Fujimaki, N., and Katayama, M. (1992). Semicond. Sci. Technol. 7, 135. Zimmermann, H., and Ryssel, H. (1992a). Appl. Phys. A 55, 121. Zimmermann, H., and Ryssel, H. (1992b). J . Electrochem. SOC. 139, 256.

St MlCONDliC rORS A N D SEMIMETALS. VOL 42

CHAPTER 6

Some Atomic Configurations of Oxygen B . Pajot CROUPE DE PHYSIQL'E DES SO1 I D t S U N I V E R S I T ~DE PARIS, PARIS. FRANCE

1. 11.

111.

IV.

V.

VI.

VI1.

INTRODUCTION . . . . . . . . . . . . . . . . . . . SPECTROSCOPY OF LOCALIZED MODESI N SEMICONDUCTORS . . I . Localized Mode.\ und Resonant Modes . . . . . . . 2. Intensities . . . . . . . . . . . . . . . . . . . 3 . Stress-Induced &ffects , . . , . . . . . . . . . . INTERSTITIAL OXYGEN, . . . . . . . . . . . . . . . I . Staric Properties . . . . . . . . . . . , . . . . . 1. Dynamic Properries . . . . . . . . . . . . . . . 3 . Perrurhation hy Foreign Atoms . . . . . . . . . , . Q~~ASI-SUESTITUTIONAI OXYGEN. . . . . . . . . . . . I . Spectroscopies o / rhc Oxygen-Vacancy Defect . . . . 2 . Thermal Stability , . . . . . . . . . . . . . . 3 . Other 0-Related Irradiation Defects . . . . . . . . COMPARISON W I T H OTHER LIGHTELEMENT IMPURITIES . . . I . C'urbon . . . . , . . . . . . . . . . . . . . . 2 . Nitrogen . . , . . . . . . . . . . , , . . , . . 3 . Hydrogen . . . , . . . . . . . . . . . . . . . OXYGEN I N OTHER SEMICONDUCTORS . . . , , . . . . . 1. Germanium . . , . . . . . . . . . . , . . . . . 2 . Gallium arsenidt. , . . . . . . . . . , . . . . . SUMMARY . . . . . . . . . . . . . . . . . . . . Acknondedgments . . . . . . . . . . . . . . . . . Referenc,es . , , . . . , . . . . . . . . . , ,

191 i94

194 196 196 200 200 210 21 I 217 217 220 222 224 224 226 228 233 213 236 243 244 245

1. Introduction

Oxygen is present in silicon crystals grown by the Czochralski 1CZ) pulling technique from a silica crucible (Chapters 2 and 7). It is also present in float-zoned (FZ) material refined under vacuum, but there the residual background is on the order of 10l3atoms/cm3 compared to about atoms/cm' in the CZ material. The affinity of oxygen for silicon can be explained by the strength of the Si-0 bond (-5.6 eV in molecules like HOSi (CHJ3), which i s stronger than the Si-Si bond ( - 2 . 3 eV in silicon). The infrared (IR) absorption measurements (Jastrzebski et a]. , 1982; Pajot et al., 1985) also show that most of the oxygen present in as-grown CZ 191 Copyright 0 1994 by Academic Pies\. Inc All nghts of reproductlon In any form reserved ISBN 0-12-752142.9

192

B. PAJOT

silicon at room temperature is in a dispersed form, labelled interstitial oxygen (O,), the structure of which will be presented in due time. Near the melting point of silicon (1412°C) the solubility of oxygen is estimated to be 2.1 x 10l8 atoms/cm3 (Carlberg, 1986). The temperature dependence of the solubility shows some scatter (Mikkelsen, 1986), but it none the less indicates that the equilibrium solubility at room temperature is smaller by several orders of magnitude than the concentration of dispersed oxygen in as-grown crystals. This means that as-grown CZ silicon is oversaturated with oxygen at room temperature and, as a consequence, annealing of the material can produce the precipitation of oxygen into various forms of silica (SiO,) precipitates. These precipitate forms can be considered globally as a second physical state of oxygen in silicon. From an initial state where oxygen is dispersed in silicon, it is possible to reach after annealing another state where the whole oxygen content is precipitated (the exact morphology of the precipitates depends on the annealing conditions). The situation is reversible and oxygen can be dispersed again by dissolution of the precipitates at very high temperature (- 1300- 1350°C) and quenching to room temperature. At high temperature, oxygen out-diffuses from the near surface regions so that the full 0,concentration is measured only in the bulk of the material. It has been observed by high-resolution X-rays diffraction measurements (Takano and Maki, 1973) that the presence in silicon of dispersed oxygen produces a small increase of the average lattice spacing, proportional to the oxygen concentration. This increase indicates a local expansion of the lattice near the isolated 0 atom. It has also been shown that the commonest form of silica found in the microprecipitates is the amorphous phase, with a density comparable to that of silicon. Hence, whatever its form, the presence of oxygen in silicon always leads to an expansion of the material and to built-in stresses. In the case of large precipitates, these stresses can be relieved by the growth of dislocations. The precipitates are characterized by their stoichiometry, their distribution, their structure and their size. These parameters depend on the annealing conditions. A discussion of the relationship between the shape of the precipitates and their infrared absorption has been given by Gaworzewski et al. (1984). Details on the properties of the oxygen precipitates can be found in other chapters of this book. Group VI doping elements S, Se and Te, are double donors in silicon (for a review, see Wagner et al., 1984). This electrical activity is explained by a substitutional location of these elements in the same way as the single donor electrical activity of P, As, Sb or Bi. As-grown CZ silicon displays an n-type electrical activity related to oxygen (Kaiser and Keck, 1957). This electrical activity comes indeed from a series of donor cen-

6.

SOME ATOMIC'('ONFIGURATIONS OF O X Y G E N

193

ters, the so-called thermal donors (TDs), which are also double donors (Wruck and Gaworzewski, 1979). Substitutional oxygen, which is also a group V1 element. could act as a double donor on a substitutional site. This location is unstable because of the small tetrahedral radius of the 0 atom (0.68 A), but it has been argued that TDs could be due to substitutional 0 surrounded by interstitial 0 to compensate an inward distortion by an outward distortion (Keller, 1984). The total concentration of these TDs is typically less than 1%) of the total oxygen concentration in the as-grown material. The TDs are thermally unstable, and they are destroyed by annealing the as-grown material above 550°C. The same TDs can be created again under annealing in the 400-500°C range and they are sometimes labelled 450°C TD. The singly ionized state of these TDs is paramagnetic because of the presence of an unpaired electron (Muller et al., 1978). The electron nuclear double resonance (ENDOR) results on the paramagnetic state in samples enriched with isotope "0 can be interpreted by assuming that the core of the TDs contains four oxygen atoms (Michel et al.. 1989) with a C2vpoint group symmetry. On the other hand, calculations by Deak. Snyder and Corbett (1992) lead to a model of TDs involving two 0 atoms and a self-interstitial. This seems to demonstrate that the core of the TDs is not an isolated on-center oxygen atom, but the maximum number of 0 atoms in the 450°C TDs is not known. Now, it can be said that despite substantial progress, a unified picture of these donors including a full microscopic description has not yet been reached. Annealing of as-grown CZ silicon wafers for a short time at between 650 and 800°C is done to destroy the 450°C TDs produced during the cooling-down of the crystal (the annealing time decreases when temperature increases). After the destruction of these TDs, the electrical activity of CZ silicon is the same a s that of FZ silicon with the same dopant concentration. and this can be considered as a proof that interstitial oxygen is electrically inactive. If the annealing time is increased beyond a few hours, the free-electron concentration starts increasing again as a new kind of thermal donors is produced (Capper et al.. 1977; Kanamori and Kanamori, 1979). This electrical conduction has been attributed to inversion layers surrounding some silica precipitates (Henry et al., 1986). In this introduction, I have attempted to give an overview of the different states where oxygen can be found in silicon when used for technological purposes, pointing out that the isolated form is interstitial oxygen. In the next sections, I will narrow the study to the structure and dynamics of isolated and nearly isolated forms of oxygen in silicon. I will therefore extend the description to the oxygen complexes created by irradiation with energetic particles, and it will be instructive to compare these prop-

194

B. PAJOT

erties and structures with those of other light and reactive elements in silicon. I will show in the last section that the structure of the oxygenrelated centers in other semiconductors have a great similarity to the forms in silicon, but that the relative strength of the bonds between 0 and the atoms of the crystal can allow for instance the formation of OH bonds not found in silicon. A wealth of information on the structure and stability of oxygen complexes in semiconductors has been obtained from their localized vibrational modes, I will henceforth start by trying to show how the information can be deduced from the infrared vibrational spectra.

11. Spectroscopy of Localized Modes in Semiconductors

1. LOCALIZED MODESAND RESONANT MODES In semiconductors, localized defects (LDs) can produce localized or resonant vibrational modes. Most of the LDs are isolated interstitial or substitutional foreign atoms, pairs of atoms or association of a foreign atom with a lattice defect. The frequencies of the modes induced by the LDs depend on the force constants between the foreign atoms and those of the host crystal as well as on their mass differences. Sketchily, when the differences between the force constants and the masses are small, the frequencies of the modes induced by the LDs fall within the allowed frequencies of the crystal, and they are resonant with some phonon frequencies. Conversely, for large force constants or for atoms with small masses, the frequencies are higher than the Raman frequency; they cannot propagate in the crystal and remain localized near the defect, hence their name of localized modes. Representative frequencies calculations have been made for impurity pairs in silicon (Elliott and Pfeuty, 1967) and for isolated substitutional impurities in semiconducting compounds with zinc blende structure (Vandevyver and Plumelle, 1977) using Green’s function techniques. Recently, ab initio calculations of LDs structures and vibrational modes have been undertaken starting from a crystalline molecular cluster and the results of such calculations will be discussed later. LDs at high densities can also alter locally the phonon density of states of the host crystal and such accidents are observed in silicon (Angress, Goodwin and Smith, 1965). Much information has been gained from the IR study of the localized vibrational modes (LVM) due to LDs in semiconductors because they can generally be observed as sharp lines on a monotonous background. Some of the bonds in LDs can also be found in other compounds or chemicals, and the LD can sometimes be considered as a small pseudomolecule interacting with the host crystal. In semiconductors, this is the

6.

S O M E ATOMIC (‘ONFIGURATIONS OF OXYGEN

195

case for the LDs involving a H atom bonded only to an atom X of the crystal (linear molecule XH)or for an atom like oxygen bonded to two atoms of the crystal. The small-molecule approximation is especially useful to calculate isotope shifts, as simple relations used in molecular spectroscopy can be used. In the valence bond approximation, the isotope shift for the antisymmetric mode v 3 of a nonlinear molecule X Y I with symmetry Czl is given by v;/v, =

{ [ ( M , / M , + 2 sin’a)/M,yJ’/[(M,/M, + 2 ~in*a)/M,I}”~,(1)

for the substitution of atom X or the two atoms Y (molecule ( X Y z ) ‘ ) .M , and M , . are the masses of atoms X and Y , and 2a is the apex angle of the molecule. assumed to be unchanged by the isotopic substitution. When only one atom Y is changed, the isotopic shifts for the t w o symmetric modes of (XY,)’ are required (DeWames and Wolfram, 1964). In practice, for moderate shifts, the arithmetic mean of the positions for X Y 2 and (XY,)’ is a good approximation. An interesting aspect of the measurement of an isotope effect is the possibility to identify one or more atoms of a center, knowing their masses and their isotopic abundances. As crude as it looks, expression ( 1 ) allows a determination of the value of 2a and the interaction between the LD and the surrounding lattice. This is obtained from a self-consistent fit using expression ( l ) , where the mass M , of the atoms of the lattice is replaced by M y + M ‘ or by x M , ( x > 1 ) where parameters M ’ or x represent the interaction of X Y 2 with the rest of the lattice (Newman, 1973; Pajot and Cales, 1986). A comparison between the predicted values and the experimental ones can inform us of the interaction between the pseudo-molecule and the host crystal. When light elements like hydrogen, carbon, nitrogen or oxygen are involved in a LD, the use of isotopically enriched samples can provide information on the number of atoms of this element in symmetric locations of the LD. This is because, if two or more identical atoms with the same mass vibrate at the same frequency, the change of the mass of one of these atoms by isotopic substitution will change the frequency. When the LD is electrically active, a change in its charge state occurs as a function of the Fermi level in the semiconductor. This can produce a change of the frequency of its LVM related to the change in the force constants and polarization of the LD. Hence, the observation of Fermilevel dependent LVMs related to the same LD indicates an electrical activity of this LD. The LDs have a well-defined symmetry. in silicon, the maximum symmetry of a defect is that of the tetrahedral point group Td.The corresponding LVM is a threefold degenerate as it transforms under the same irreducible representation as x. .v and z . For LDs with lower symmetry (C?,,

196

B. PAJOT

for a trigonal center), the threefold vibrational degeneracy must be partially removed into a nondegenerate and doubly degenerate LVM so that two lines should be observed. A consequence of the lowering of the spatial symmetry of the LD is the existence of equivalent orientations for this defect in the crystal. For instance, a defect oriented along a (1 1 I ) axis has four possible orientations, representing a fourfold orientational degeneracy of the LD distinct from the vibrational degeneracy of the LVM. The existence of the orientational degeneracy must be kept in mind as it will be the origin of most of the effects observed when a uniaxial stress is applied to the crystal containing the LD.

2. INTENSITIES In the SI system, the integrated absorption Ai of an isotropic oscillator with reduced mass p at concentration N in a solid with refractive index n is

where E” and c are, respectively, the permittivity of vacuum and the speed of light in a vacuum. The effective charge q (in electric charge units) can be considered as a dipole moment per unit of displacement (note that expression (2) corresponds to a spectrum plotted in wavenumber units). With p in atomic mass units and q expressed in units of electron charge, q

=

4.56 x 10’. (pnAi(cm-2)/N(cm-3))”2,

Expression (2) is deduced from that given by Newman (1973), and strictly speaking, it is valid only for a center with cubic symmetry like a substitutional isolated impurity. Once the effective charge is determined for a LVM at a given temperature, a calibration factor of the absorption can be obtained. Effective charges can also be obtained from ub initio calculations by computing the change in the dipole moment of the cluster when the atoms are displaced in proportion to the normal coordinates (Jones and Oberg 1992). 3. STRESS-INDUCED EFFECTS a. Stress-tnduced

Splitting of the LVMs

A uniaxial stress applied to a crystal containing LDs produces an elastic strain that can remove part or all of the degeneracies associated with these LDs. For a substitutional impurity in a cubic crystal, there is no

6.

S O M E ATOMIC CONFIGURATIONS OF OXYGEN

I97

urientational degeneracy and the stress can partially or totally remove the threefold degeneracy of the LVM because it lowers the symmetry of the LD. For an anisotropic LD, the main effect for most of the stress directions is the partial or complete removal of the orientational degeneracy. This produces a splitting of the LVM because of the angular dependence of the coupling of the electric dipole with stress. The physical separation between the dipoles vibrating with different frequencies implies a total o r partial polariLation of the stress-split components with respect to the stress direction. When stress is applied along simple crystallographic directions, the number of stress-split components, their relative intensities and polarizations can be obtained from simple geometrical arguments considering the initial orientations of the dipoles. In the actual cases, the orientations of the dipole moments are derived from the experimental data. The splitting of the components is a bilinear function of the stress and of the piezoyxctroscopic coefficients of thc LD. For crystals with a diamond or rinc blende structure. there are five possible kinds of LDs with distinct \ymmetries. Kaplyanski (1964) has tabulated the number of components, rhc relative intensities and the polarizations for these five groups for stresses along the (100). ( 1 10) and ( I I 1) directions. He has also calculated the number of independent piezo-spectroscopic coefficients and the shifts from the zero-stress value for these five groups. We are concerned here mainly with trigonal and rhombohedric I LDs where the dipole moments are along ( I 1 I ) and (I10) directions, respectively. The number of independent coefficients are two ( A , and A : ) for the trigonal centers and three ( A , . A ? and A , ) for the rhonihohedric I centers. Tables I and 11 adapted from Bosomworth et a]. (1970). give the shifts of the stress-induced components of a LD with one of these two symmetries as a function of the orientation of stress (T. h. Dic.hroism und Atomic Rcoric~ritutiori

Under stress, previously equivalent orientations of the same anisotropic L D are distributed i n t o classes with different energies (as a rule, the highest energy is for orientations parallel to the stress). With stress applied at a low temperature, there is no change in the population of the different orientations to minimize the LD energy because atomic reorientation requires energy taken from the lattice phonons. When stress is applied at a temperature where thermal energy allows reorientation of the LD and when the sample is cooled under stress, the low-temperature population of the orientations with the lowest energy is enhanced. The \tress can be released at a low temperature as the populations are frozen.

198

B. PAJOT

TABLE I REMOVING OF THE FOURFOLD ORIENTATION DEGENERACY OF A LVM RELATED TO A ( I 1 I)ORIENTED CENTER FOR DIFFERENT ORIENTATIONS OF A UNIAXIAL STRESS u (THE RESIDUAL DEGENERACY Is NOTEDR). THESHIFT A PER UNITSTRESS OF A COMPONENT WITH RESPECT TO THE ZEROSTRESS POSITION Is GIVENAS A FUNCTION OF THE INDEPENDENT PIEZO-SPECTROSCOPIC COEFFICIENTS A, A N D A2. THERELATIVE INTENSITIES I FOR DIPOLES P OR u AREGIVEN FOR 4 1 OR 1 TO u OR PARALLEL TO SPECIFIC ORIENTATIONS. 111 : I 1

u parallel to

A

R

[1101

A , + A2 A, - A2

2 2

P

U

P

U

2: 1:o 0:1:2

1:2:3 3:2:1

TABLE I1

REMOVING OF THE SIXFOLD ORIENTATIONAL DEGENERACY OF A LVM RELATED TO A (110)ORIENTED CENTER FOR DIFFERENT ORIENTATIONS OF A UNIAXIALSTRESS u (THE RESIDUAL DEGENERACY Is DENOTED R). THESHIFT A OF A COMPONENT WITH RESPECT TO THE ZERO STRESS POSITION Is GIVENAS A FUNCTION OF THE INDEPENDENT PIEZO-SPECTROSCOPIC COEFFICIENTS A , , A A N D A,. THERELATIVE INTENSITIES I AREGIVENFOR DIPOLES p PARALLEL TO (1 lo) OR TO (100) WITH THE ELECTRIC VECTOROF THE RADIATION Ell OR I TO u OR PARALLEL TO SPECIFIC ORIENTATIONS.

[lo01

[I111

11101

4 2 3 3

1

4 1

A2 A,

(A, (A,

+ 2 ’ 4 2 + 2AJI3 + 2A2 - 2A,)13

A2 + A3 (AI + A d 2 A2 - A3

2: 1 0: 1 4: 1 0:3

0: I

I:O:O

0:l:O 2:0:2 0:l:O

l:2:l 0:o: I

1

:o

1:l 1:l

6.

SOME ATOMIC CONFIGURATIONS OF O X Y G E N

199

The population difference reflects on the dichroism of the sample measured by 9 = (a1 - all)/(aL+ all), where a I and all are the absorption coefficients measured for radiation polarized respectively perpendicular and parallel to the initial stress. We consider as an example ( I 1 I)-oriented dipoles forced to reorient under a ( 1 10) stress: the four orientations with initial populations no are converted into two orientations with population H , , , ~ ~ ,and two with population n L ( o w )It. can be checked that here, 9 = ( n , - nL)/2n,,.After removing the strain, the dichroism is maximum (ao). Assuming a first-order kinetics for the return to equilibrium, &d/df = -4k,@,

(3)

where kR is a thermally activated reorientation rate. At temperature T . it can be written k, = vO exp[ - ER/k,T], where vo is an attempt frequency and ER is the energy required to reorient the LD. After annealing at temperature 7 during time t . the dichroism decreases to 9 = 9" exp[ - 4kRf]. Successive isothermal annealings allow us to determine k,. An independent determination of vo and ER is obtained by repeating the procedure at different temperatures. Atomic reorientation of the oxygenvacancy center has been observed by EPR and by IR absorption (Watkins and Corbett; Corbett et al.. 1961).The measurement of atomic reorientation of interstitial oxygen in silicon and germanium (Corbett et al., 1964a) enabled a spectroscopic determination of the diffusion coefficient of oxygen in these semiconductors as atomic reorientation is the first step of diffusion (see also Chapter 8 ) . c'.

Dicliroism und St ress-Depcnden t Currier Capt ure

In a semiconductor, an electrically active LD has at least one level in the band gap. The energy of this level is also stress sensitive. Let us consider an LD with an electron acceptor level deeper than that of shallow donors. If the sample contains shallow donors at a concentration smaller than that of the LD. all the donor electrons are trapped at the acceptor level of the LD, and some of the acceptor levels remain empty. If such a sample is cooled under stress from a temperature where the electrons are not yet trapped by the acceptor level, the electrons would be progressively trapped, starting at the levels made deeper in the band gap by the stress. Hence the more shallow levels will remain empty or partially filled. The measurement of a I and all at LHeT after removing the stress will also show a dichroism due to stress-dependent electron capture. An analysis similar to the one made for atomic reorientation gives the thermalization energy of the electron in the conduction band, which is a value close to that of the electron acceptor level. Such a

200

B. PAJOT

stress-dependent electron capture has been observed for the neutral oxygen-vacancy center in silicon (Watkins and Corbett; Corbett et al., 1961).

111. Interstitial Oxygen

1. STATIC PROPERTIES Direct evidence for interstitial oxygen in silicon comes from the observation of its vibrational modes. They have first been detected by infrared absorption (see also Chapters 3 and 4). Phonon spectroscopy using superconducting tunnel diodes has also been used, and a brief description of this technique and its possibilities is given at the end of the paragraph. The infrared studies of Hrostowski and Kaiser (1957) using "0-enriched samples (the normal percent abundances of the 0 isotopes are I6O:99.76, "0 :0.04, "0 :0.20) showed that three vibrational features were associated with oxygen in as-grown silicon. They were then attributed to the three modes of a nonlinear Si-0-Si pseudo-molecule with Cz,, symmetry embedded in the silicon lattice. The most intense line, located at 1136 cm-' at liquid helium temperature (LHeT), was ascribed to the antisymmetric mode v 3 of Si-I6O-Si. Two other lines at 517 and 1206 cm-' were ascribed to the two symmetric modes of this Si-0-Si pseudo-molecule. In this pseudo-molecule, the Si atoms were assumed to be nearest neighbors atoms of the crystal, and the bridging with the 0 atom resulted from breaking the Si-Si bond. In this configuration, the interstitial 0 atom is located in a (111) plane equidistant between the two Si, atoms and its exact position depends on the Si-0-Si angle (Fig. I). A confirmation of this kind of interstitial structure came from the observation of the Si isotope effect of the v3 mode. Figure 2 shows the absorption of this mode at LHeT in a sample enriched with "0 and "0: the main absorption features near 1136, 1107 and 1084 cm-' are due to the 0 isotope effect, and their intensities are proportional to the concentrations of the different 0 isotopes. The structure seen for each 0 isotope is due to the isotope effect (silicon has three isotopes, 28Si,29Siand 30Si,with respective percent abundances of 92.17, 4.71 and 3.12), and the relative intensities of the components correspond to 28Si20,28Si029Si and 28Si030Si.The intensities of the other Si isotopes combinations are too small to be seen here. Incidentally, this figure illustrates an interesting, but unexplained feature: while the lines for l 6 0 and "0 have a FWHP of 0.6 cm-', the one for "0 is -1.2 cm-I (the only difference between "0 and the other isotopes is its nonzero nuclear spin (5/2)). This observation first made on standard CZ samples is independent of the samples used (Pajot, 1986). When cor-

6.

20 1

SOME ATOMIC CONFIGURATIONS OF OXYGEN

tic,. I . Model of a silicon unit cell containing an interstitial 0 atom (dark gray). This representation takes into account the actual distortion of the first neighbors of 0 along a ( I I I ) axis.

L

1070

10%I

III 0

I130

1150

\ ~ ' 4 L ' I ~ N l ~ h l R l(cm-1) iR FIG. 2 . Absorption o f vl(Oi)at h K i n ;I silicon sample enriched with "0 and ''0. 'The low-energy satellites are due to 'xSiO"Si and "Si0'"Si combinations. Note the broadening of the "0,mode (Pajot 1988).

rected for the intensity of the wing of the 2xSi2'60 line at the position of the small lines. the experimental relative intensities of the components match the calculated ones. This comparison was considered by Pajot and Deltour (1967) as proof that the 0 atom was bonded to two Si atoms. A similar conclusion was also reached by Bosomworth et al. (1970). When the temperature is raised above 8 K. new lines appear on the low-energy

202

B. PAJOT

side of the 1136 cm-' line (Fig. 3). These lines were attributed to transitions from thermalized levels close to the ground state (Hrostowski and Alder, 1960), but no quantitative level scheme was provided at that time. At room temperature, only one broad absorption band is observed near 1106 cm-' with a FWHP of -30 cm-'. This band is probably the superposition of sharper thermalized components originating, as will be shown later, from the low-frequency vibration-rotation motion of the 0 atom in the (1 11) plane. This is substantiated by the asymmetric profile of the band and by a noticeable shift of the peak absorption with temperature (Schomann and Graff, 1989). The attribution of the line at 1206 cm-' to a symmetric mode of 0;was questioned by Chrenko, McDonald and Pel1 (1969, who suggested that it was indeed related to a combination of the v3 mode with the libration of the 0 atom about the (1 11) axis containing the two Si atoms. The confirmation came from the thorough investigation of Bosomworth et al.

FIG.3 . Absorption of u3(l6Oi)in silicon at between 15 and 100 K showing the progressive thermalization of the low-frequency excited levels (K. Krishnan and S. L. Hill (1981). In Fourier Transform Infrared Spectroscopy, H. Sakai (ed.), p. 221. S.P.I.E., Bellingham, Wash.). Compare with Fig. 2 .

6.

SOME ATOMIC CONFIGURATIONS OF O X Y G E N

203

WAVENUMBER (cm-1)

FIG. 4. (a) Low frequency absorption of "0,in silicon due to the transition from the ground state to the first excited state of the two-dimensional oscillator. The FWHP of 0.2 c m - ' is resolution limited. (b) The same absorption at 35 K , showing transitions from thernialized levels. ( c ) .4bsorption of a 'XO-enrichedsample (from D. R . Bosomworth, W. Hayes. A. R . L. Spray and G. D. Watkins (1970). Proc. Phys. Soc. London A 317, 133).

(1970), who reported the observation of a low O-related frequency vibration at 29 c m - ' for I6O and 27 c m - ' for I80at LHeT (Fig. 4a and 4c). The corresponding mode for "0 has also been observed at 28 cm-' (Pajot, 1988). Bosomworth et al. (1970) explained the mode at 29 cm-' by a lowfrequency vibration of the 0 atom in the ( I 11) plane perpendicular to the Si . . Si broken bond. The motion of the 0 atom in this plane can be

204

B. PAJOT

considered either as a perturbed two-dimensional (2D) oscillator vibration or as the combination of a nearly free rotation about the Si . * . Si axis and of a low-frequency vibration of the 0 atom in a (211) plane. In the first case, a given state is labeled by quantum numbers v = v , + v2 and I = v I - v2. The IR selection rules are Av = I , A1 = ? 1 and the transitions are polarized in the two-dimensional oscillator plane. In this framework, the low-frequency mode observed at LHeT is the 10, O> + I I , t I > transition. In the second case, the formalism for the vibrationrotation interaction can be used: the vibrational state is a symmetric mode u2 of the Si-0-Si quasi-molecule described by a vibrational quantum number n (to avoid the confusion with v used previously) and the rotation about the Si . . . Si axis by a rotational quantum number J . At LHeT, the only transition observed is A n = 0, A J = 1 . It corresponds to a one-quantum excitation of the rotational motion of the 0 atom in the ( 1 1 1 ) plane about the broken Si . . * Si axis. At temperatures above LHeT, Bosomworth et al. (1970) also observed far IR lines corresponding to thermalized levels for the low-frequency excitations (Fig. 4b). They related these transitions with the ones near 1136 cm-’, and they could derive from both sets of data a unique energy level scheme. These two models give nearly identical values of the apex angle 2a of the Si-0-Si group (= 162”). Assuming an unaltered bond length of I .6 A for Si-0, the distance between the two bridged Si atoms is then 3.16 A compared to a nearest neighbors distance of 2.35 A in the unperturbed silicon lattice. The expansion due to oxygen must be partially compensated by a compression of the neighboring Si-Si bonds, and this explains why an average increase of the lattice constant of silicon is observed with increasing concentrations of interstitial oxygen. A more sophisticated phenomenological model of the vibration of 0, in silicon (but physically equivalent to the preceding) has been worked out by Yamada-Kaneta, Kaneta and Ogawa (1990) using a Si, = Si-0-Si = Si, pseudo-molecule with point group symmetry D3d.These authors consider the Hamiltonians for the unperturbed motion of the 0 atom in the ( I 1 1) plane and for the antisymmetric 0 mode (irreducible representation A2,, of D3J along the ( 1 1 I ) axis coupled by an interaction term. In the interaction scheme, a state is described by Jk, I , N > , where k describes the radial dependence of the two-dimensional anharmonic excitation, I , its angular dependence and N , the high-frequency A , , mode. In this description, the 29, 1136 and 1206 cm-’ lines correspond, respectively, to the transitions from the ground state 10, 0, O> to the 10, I , O>, 10, 0, I > and 11, 0, 1 > states. The calculation of the eigenvalues of the Hamiltonian as a function of the adjustable parameters was performed self-consistently using experimental frequencies for I6O and l8O. The

*

6.

205

SOMF 4lOMIC' CONFIGURATIONS O F OXYGEN

IABLE 111

ASSOCIATED WITH BFTWEEN EXPFRIMFNTAI F R I QlJFNC I F 5 (Cm I ) FOR TRANSITIONS %1,0I N S i r r c o r u roR T H E DIFFFRFYT i)ISOTOPFS A N D THOSE ( I N B H A C K E T S ) CAICULATED B> Y ~ M A D A - K A N FFTTAAI (1990) T t r i S I X cm ' MODE Is NOT INCIUDED THE I N I T I ~ L ( I ) 4 h l ) F I N A l ( f ) S T A T E S OF THE TRANSIIIO ARE NSINDICATFD W H E N A V A I L A B L F , E X P E R I M E N T A I ERLQIIEMIFSFOR "0 H A V FALSO B E IN G I V F N ( OMPARIWN

1

10. 0. 0 >

10.

?

I. 0

'

10. 0. I-> /I.0, I>

29.33

28.P

27.2"

129.41 I 136.4 I 1135.7)

1109.5'

"7.51 1085.0' 11084.I I

[ 1203.8)

I IS I . I" [ I 148.51

37.8" 137.21

35.2" [34.7]

1203.7'

117f1.7~

128.3' 127.71

I 101.3d

216.7' 216.51

I192.6d

1077.6" 1077.7 I 1161.31

1071 8d [ 1072.hl "Bosomworth et al. (1970). hPa;ot I1988). 'Pajot and Cales (1986). "PdjOt (1986).

overall agreement with the experimental values of the frequencies of the transitions given in Table 111 is good. For N = 0, the equilibrium positions of the 0 atom with respect to bond-center (BC) location are 0.25 and 0.24 A for I6O and "0,respectively. For N = 1 , these values increase to 0.34 and 0.32 A. An interesting result of the calculations by YamadaKaneta et al. ( 1990) is that the phenomenological coupling constant between the A,,, mode and the 2D low-frequency motion (2DLFM), used to fit the data. is found to be negative. Now, in the interaction scheme, the radial dependence of the force constant of the Az,, mode (labeled u3 for convenience) is proportional to this coupling constant. It follows then that, when the distance of the 0 atom from the BC position increases. the frequency of ui should decrease. A best fit analysis of the Si and 0 isotopic shift of the u3 components has also been performed using a simple molecular model by adjusting the lattice interaction through an adjustable

206

B. PAJOT

mass M' added to that of the Si atoms and the Si-0-Si angle 2a (Pajot and Cales, 1986). A value of 3 amu is obtained for M' and the value of 164" for 2a is about the same as the one obtained by the other methods. The frequency of the Oi-related mode at 517 cm-' is less than the Raman frequency of silicon (524 cm-' at LHeT at the Brillouin-zone center). Piezo-spectroscopic measurements on this mode (Stavola, 1984) indicate that the components of its dipole moment transform like coordinates x and y in the (1 11) plane (coordinate z is chosen along the trigonal ( 1 1 1) axis). Consequently, this mode can be labeled by the doubly degenerate representation E,, of point group D3d. From the fact that (i) no O-isotope effect is observed for this E, mode and (ii) no Si-isotope effect is observed for the 2DLFM, it is assumed that the coupling between these two modes is negligible. It turns out that the 518 cm-' line is very close to the Raman frequency of silicon. The E,, mode (labeled uI for convenience) is attributed to an in-band O-induced resonance (Angress et al., 1968). A weak line at 1013 cm-' has been ascribed to an overtone of u I (Pajot and Cales, 1986). A weak 0,-related line is also observed at 1725 cm-' at room temperature (Lappo and Tkachev, 1970; Pajot et al., 1985), shifting to 1749 cm-' at LHeT (Krishnan and Hill, 1981; Pajot and Cales, 1986). The frequency seems too small to ascribe this absorption to an overtone of v3: this would imply an unusually large anharmonicity of u3 and an overtone/ fundamental intensity ratio larger than the intensity ratio observed (1.6 x lo-'). The temperature dependence of the structure of the new absorption is similar to that of uj: thermalized lines appear above 10 K and the absorption shifts to 1720 cm-' at room temperature. The energy difference ( ~ 6 1 3cm-') between the new absorption and v3 is constant and temperature independent. This value compares with the energy of the two-phonon TA + TO mode at the X point of the Brillouin zone of silicon. Therefore, it seems sensible to ascribe the 1749 cm-' line to a combination mode of u3 with the earlier lattice phonon combination (Pajot et al., 1985). The Si isotope shift of the new line is however -3.5 times larger than that of v3, and this implies a strong coupling of the lattice phonons with the nearest neigbors of the 0 atom that is not expected at first sight. The vibration of 0; in silicon has also been detected by phonon spectroscopy (Dittrich, Scheitler and Eisenmenger, 1987). In this method, a superconducting Al-insulator-A1 tunnel diode acting as an acoustic phonon generator is evaporated on one side of an O-containing silicon sample. The frequency of the phonons emitted is tuned by changing the generator voltage. An Sn-insulator-Sn superconducting junction evaporated on the opposite side of the sample acts as a detector (the typical sample thickness is 1-2 mm). With this combination of junctions, the useful

h.

800

SOME ATOMIC CONFIGURATIONS OF OXYGEN

900

1000

1100

1200

207

1300

PHONON FREQUENCY (GHz) FIG. 5 . Phonon absorption spectrum at I K of the ZDLFM of '*O,In nuturd silicon. The contribution of I6O,has been computer subtracted for clarity. The converted FWHP of the '*O, absorption is 0.13 cm-I. The high-energy satellites are attributed to 0, pairing ( E . Dittrich. W. Scheitler and W. Eisenmenger (19871. Japan. J . Appl. Phvs. 26, Suppl. 26-3,

R73).

phonon spectrum is 280-3000 GHz (9.3-100 cm-I). The acoustic phonons can be resonantly absorbed in the silicon sample, and this produces dips in the phonon power spectrum detected. Two absorption dips are observed with a standard CZ silicon sample: The stronger one at 875 GHz (29.14 c m - ' ) and a weaker one at 823 GHz (27.41 cm-I) corresponding respectively to the ZDLFM of IhOand I8O. In this spectral range, phonon spectroscopy is more sensitive by two orders of magnitude than IR absorption (Fig. 5 ) . An nh initio calculation of the LVM of interstitial oxygen in silicon has been made by Jones, Umerski and Oberg (1992) using a crystalline molecular cluster of reasonable size (OSi,H,2) centered on an interstitial 0 atom. After relaxation of the atoms of the inner Si, = Si-0-Si = Si, group, energy convergence is obtained for some values of the bond angles and interatomic distances. These are given in Table IV with the calculated frequencies. The agreement for the antisymmetric mode is very good. From this calculation, v l should correspond to the symmetric stretching mode calculated to vibrate at 554 cm I, as the displacement of the 0 atom for this mode is found to be negligible. This last result can explain why no 0 isotope effect is observed for this symmetric mode. The frequency of the 2DLFM is very sensitive to the size of the cluster, and it is outside the range of applicability of the method used. The effective ~

208

9. PAJOT

TABLE IV AB INITIOATOMIC PARAMETERS AND FREQUENCIES (cm-I) FOR INTERSTITIAL OXYGEN I N SILICON (Jones et al., 1992). EXPERIMENTAL VALUES AT LHeT AREGIVEN I N PARENTHESES. THEMODE LABELS ARERELATED TO THOSE OF A CzvMOLECULE FOR CONVENIENCE.

VI

1 I04 (1136)

1051 (1085)

I098 ( I 129)

554 (518)

553 (518)

534 -

Si-0 length: 1.59A Si . . . Si length: 3.19A SiNN-SiNNN: 2.26A Si-0-Si angle: 172" ( 162")

charge of the antisymmetric mode at 1104 cm-' is calculated to be 3.5 e for a dipole moment parallel to (11l), close to the experimental value of 3.8 e calculated using expression (2). Experimentally, for an integrated absorption of v 3 normalized to unity, approximate relative intensities at LHeT of v , , u3 + one 2DLFM at 1206 cm-' and of the 2DLFM excitation at 29 cm-' are 0.25, 0.034 and 0.005, respectively (Pajot et al., 1985; Pajot and Cales, 1986). The stability of structures containing more than one Oi has been calculated by Needels et al. (1991). They found that only two adjacent Oi in a staggered structure are more stable (by about 1 eV) than two isolated Oi. The calculations show that chainlike clusters of several adjacent Oi along ( I 10) directions can also be stable. The thermodynamic conditions for the production of two-atom clusters is a compromise between a minimum annealing temperature for appreciable hopping of Oi (>900 K) and a maximum temperature (= 1000 K) where dissociation reduces the clusters concentration. The separation between the isolated Oi v 3 mode and the one for the 0;pair is evaluated to =20 cm-', and it is suggested that the latter could be observed at a low temperature above the isolated Oi frequency. Satellite lines (Fig. 5) have been ascribed to the shift of the 2DLFM of Oi due to the statistically distributed Oipairs (Dittrich et al., 1987). The measurement of the stress-induced splitting of the Oi lines and of the polarization of the components have provided fundamental information on their origin (Bosomworth et al., 1970). These results have been implicitly used in the preceding description of the structure and vibration of Oi, and they have reconfirmed that the dipole responsible for v3 is a (1 1 1)-oriented T dipole. The splittings of the Oi mode at 1206 cm-' shown

6.

SOME ATOMIC CONFIGURATIONS OF OXYGEN

-1

209

onentat ions

0

20

40

STRESS (kgOrnm2)

FIG.6 . Stress-dependent splitting of the 1206 c m - ' line of 0,in silicon at 20 K: (a) ull[ l 0 l . (b) ~y(ll1101.( c ) nll[l I I]. The orientations of the contributing dipoles are indicated (D. R . Bosomworth. W . Hayes, A. R . L . Spray and G . D. Watkins (1970). Proc. Phys. Soc. London A 317, 133). I kgf mm-? is approximately 10 MPa.

in Fig. 6 differ from those for a u dipole perpendicular to the ( 1 11) axis (Table I), and they also confirm the attribution of this mode to a combination involving the IT dipole of the antisymmetric O imode. It is interesting to note that when the stress is applied along a given ( I 1 I ) axis, the frequency of the vibrating dipole oriented along this axis decreases. This can be related to the nonlinear structure of the Si-0-Si group as a stress along the Si . * . Si broken bond must decrease the apex angle. In the simple quasi-molecule model, a decrease of CY. in expression ( I ) without any change in the force constants must produce a decrease of the v3 frequency. The effect is also consistent with the negative value of the coupling constant obtained by Yamada-Kaneta et al. (1990) for the interaction between v 3 and the 2DLFM. These explanations are only phenomenological, and the physical reasons lie in the electronic properties of the center. The values of the piezo-spectroscopic coefficients for the different 0, lines obtained by Bosomworth et al. (1970) are given in Table V .

210

B. PAJOT

TABLE V PIEZO-SPECTROSCOPIC COEFFICIENTS A, AND A 2 FOR THE DIFFERENT O i L i ~ IN ~ sSILICON (Bosomworth et al., 1970). Line (cm-')

A,((cm-'/GPa)

A2 (cm-'/GPa)

518 (20 K) 1136 (20 K) 1206 (20 K) 29 ( 4 K)

-1.1 0.2 ? 0.1 -0.9 ? 0.2 -3.8 ? 0.3

-0.3 -0.2 2 0.1 -2.3 2 0.3 -3.8 2 0.3

2. DYNAMIC PROPERTIES Reorientation of Oi in silicon has been detected by measuring the stress-induced dichroism of the Oi lines (Corbett et al., 1964a; Stavola, 1984; Oates and Stavola, 1987). In these experiments, an oriented sample is annealed for typically 30 minutes near 400°C under a stress u of 280 MPa. The sample is then cooled under stress to room temperature, where reorientation is blocked (in this particular case) and the stress released. The results showed that the dichroism 9 defined previously (i.e., the reorientation) was maximum for oil( 111) (Fig. 7) and not detectable for u11(100). The absence of dichroism for u11(100) indicates that the defect

1040

1100

1140

WAVENLTMBER (cm-1) FIG. 7. Stress-induced dichroism of v3(Oi)in silicon at ambient for a 270 MPa ( 1 1 1 ) aligning stress. Elland E , indicate the polarization directions parallel or perpendicular to the aligning stress (J. W. Corbett, R. S. McDonald and G . D. Watluns (1964). J . Phys. Chem. Solids 25, 873).

6.

SOME A'IOMI( CONFIGURATIONS OF OXYGEN

21 1

has (1 I I ) symmetry. The sign of the dichroism depends on the orientation of the dipole p : it is positive for v7 (pII( I 1 I)) and negative for u , ( p l ( l I I)). The recovery of the stress-induced dichroism allowed to measure a reorientation energy of 2.56 eV for the jump of an 0 atom from one orientation to an equivalent one (Corbett et al., 1964a). This energy is in good agreement with the one (2.5 eV) derived from the internal friction measurements of Southgate (1960) in 0-containing silicon. In this particular experiment, the relaxation of a mechanical excitation was followed vs. temperature. A loss peak was found at high temperature (-1050"C), and it was absent for mechanical excitation along a (100) axis. The jump of the 0 atom is the first step of its diffusion, that leads to the production of centers with more than one O atom and to the precipitation of silica.

3 . PERTURBATION BY FOREIGN ArOMs Oxygen has an electronegativity of 3.44 in Pauling's scale, and it can interact with atoms with small electronegativity. It has also been shown that 0, produced a local outward distortion of the silicon lattice so that the lattice energy can be reduced by interaction with atoms having m a l l radii. Examples of these two situations follow. (1.

Lithirrin

In silicon, Li is a fast-diffusing element acting as a shallow interstitial donor. Isolated Li can pair with 0,to form LiO complexes (Pell, 1961). The hydrogenlike IR electronic spectra of isolated Li and LiO donors due to transitions from the ground state to excited states have been reported by Aggarwal et al. (1965). The existence of several shallow L i 0 donor complexes came from the observation by Gilmer, Franks and Bell ( 1965) of distinct IR electronic spectra in Li-diffused 0-containing silicon. These results showed also that these complexes were not stable with time at room temperature. In FZ silicon. where the 0 concentration is small, only one L i 0 complex containing one 0 atom is predominant (Fig. 8 ) . This complex is responsible for the ESR line measured at 27 K at g = 1.9985 reported by Goldstein ( 1966) in Li-diffused samples and for the LiO electronic spectrum studied by Jagannath and Ramdas (1981)in similar samples at LHeT. When Li is diffused in CZ silicon to study LVM absorption, p + starting material must be used. This is to avoid the excess n-type doping that produces the strong electronic background of the L i 0 donors in the spectral region where the 0, LVMs are observed. In this material, Chrenko et al. (1965) observed at LHeT ii strong and broad (FWHP = 3 cm I ) LVM at 1016 c m - ' and u3 of isolated 0, with a small intensity (Fig. 9 ) .

212

B. PAJOT

20

24

28

32

36

40

PHOTON ENERGY (rneV)

9- 8-

-

6

v

+

4.4 x 10"cm-'182%8")

Lit 4 . 4 ~ 1 0 ~ ' c m - ' ( 9 4 % ~ i ~ )

o

-7r10'~cm-' I = 0.205 cm 7 - PUMPED HELIUM

8-

-

G -

+I--

L

SAMPLE 4

6-

-

5-

Si-O

z

g 2 $ 3

1136.0

4--

I

3-

-

2-

11342

II

Li -0

1016.6

I

P

44

6.

SOME ATOMIC' CONFIGURATIONS OF OXYGEN

213

The new mode was attributed to u3 of 0; paired with a Li' ion as this center forms at the expense of isolated Oi. New lines at 525 and 537 cm - I were also reported and ascribed to 'Li and 'Li counterparts of v I . However, experiments by other groups (Spitzer and Waldner, 1965: Devine and Newman, 1970) have shown that the two low-frequency lines were actually due to a resonant mode of the Li ion of the Li+B- pair so that there is no LiO, analog of u , for Oi. The Li isotope shift of the LVM at 1016 cm-' is very small, indicating that the motion is mainly 0 related and confirming the perturbation of 0; by Li. The structure of the most abundant LiO complex is not yet known with certainty: Chrenko et al. (1965) suggested a Li ion located in the same ( 1 11) plane as the interstitial 0 atom. Such a location does not seem to be compatible with the result of the stress splitting of the electronic spectrum of the most abundant LiO donor complex (Jagannath and Ramdas, 1981) as it indicates a (100) symmetry of the complex when neutral. The binding energy of the average Li + 0 complex is 0.42 eV. and it is electrostatic. It must be less when Li is neutral. This should be the reason w h y the LiO complexes have been found to be more stable in B-doped silicon, where they are ionized, than in uncompensated material, where they are neutral (Chrenko et al.. 1965). In silicon, Mg is also an interstitial (double) donor (Franks and Robertson, 1967), and several Mg-related donor complexes are known (Lin, 1982). From the similarity of their properties with the LiO complexes. it is likely that some of these complexes are due to the electrostatic pairing of Mg with interstitial 0. h. H y d r o g e n It was shown previously that several kinds of LiO donors can be produced by the trapping of Li, by 0,.It can be thought that a similar interaction could also occur with hydrogen. A donor HO center of a different nature has also been reported to exist in germanium (Haller, 1978). However, a cluster calculation of the structure and stability of an OH center in silicon shows that no OH bond is formed (Artacho and Yndurain, 1989). This result is confirmed by the investigation of the interaction of H with 0; by Estreicher (1990) using a h i n i f i o Hartree-Fock methods. One of the results of this study is that if H is placed in one of the interstitial tetrahedral sites nearest to 0,.the minimum energy is obtained when y H (Fig. 10a). The comparison of different the 0 atom points u ~ w from structures shows that the most stable one is Oi with a BC H atom bonded to one of Si atoms nearest neighbors of 0 (Fig. lob) and that the configuration where a OH bond is formed (Fig. 1Oc) is unstable. Proportionality has been reported between the intensity of weak LVMs observed near

214

B. PAJOT

FIG. 10. Compared stabilities calculated for (0, H) configurations in silicon in a {IIO} plane (S. K. Estreicher (1990). Phys. Rev. B 41, 9886). Shaded circles: Si atoms; dotted circle: 0; solid circle: H. (a) The H atom displaced from a T site by 0.24 A and an interstitial 0 atom correspond to a local minimum of the potential energy surface (PES). (b) H near a BC position and 0 near its usual interstitial site show a minimum of the PES of -0.66 eV with respect to (a). (c) A threefold coordinated 0, it is not stable (5 eV above (a)). The dashed open circles are the locations of the Si atoms in pure silicon.

2123 and 2192 cm-' and the Oi concentration in FZ material grown under a H, atmosphere (Qi et al., 1985), and it is possible that one of these LVMs correspond to the BC H atom of Fig. lob. c . Carbon

Carbon has been for some time a major residual impurity substituting a Si atom at a level of =5 x 1016 atoms/cm3 in CZ silicon grown from pullers with unshielded S i c heaters. It produces a LVM at 608 cm-I at LHeT (Newman and Willis, 1965). Pairing of C with Oi has been reported to give a LVM at 1105 cm-' (Newman and Smith, 1969). No C-isotope shift has been observed for this LVM and it correlates with LVMs at 589, 640 and 690 cm-' ( X , Y and Z , respectively) that exhibit a C-isotope shift (Fig. 11). The 1105 cm-' LVM was ascribed to vj(Oi) perturbed by carbon. The existence of X , Y and Z was ascribed to the vibration of the perturbing C atom nearby of Oi in a site of low symmetry that can split the triply degenerate C LVM. The C atom has a small radius that produces a

6.

215

SOME ATOMIC' ('ONFIGURATIONS OF OXYGEN

local inward lattice distortion (Baker et al., 1968). Its substitution near 0, certainly reduces the outward distortion brought by 0,. and this can be the origin of this complex. Another carbon-oxygen complex is also present at a lower concentration than the preceding one, giving a perturbed 0, mode at 1052 cm and carbon modes at frequencies higher

'

WAVI:NIJM131 K ( c n - 1 )

1000

1040

1080

1120

1160

1200

1240

WAV1~;NIIMBIIK (cm-1)

FIG. I I . Absorption near L H e T of a C% silicon sample with 0, and either '*C or "C: (a) jhows the isolated 0, u , mode. the wbstitutional C (Cs) L V M and L V M s X , Y and Z due 10 0, perturbed by C,; (b) shows the first overtone of "CS, isolated 0, modes and lines A and B . due to 0, modes perturbed by carbon (Claybourn and Newman 1988). Line A at 1105 cm and modes X , Y and Z are due to the same center. All the concentrations are of the order of I x IOln atomsicm'.

'

216

B. PAJOT

11364 1 II

4.5 B

WAVENUMBER (cm-1)

FIG.12. Ge-concentration dependence of the perturbation of v3(Oi)in silicon by Ge. The two perturbed modes are labeled 0,-I1 and 0,-111 (H. Yamada-Kaneta, C. Kaneta and T. Ogawa (1992). Materials Science Forum 83-87, 419). 1 ppma corresponds to 5 x 10l6 atoms/cm3.

than those of X , Y and Z , but there is no microscopic model for this center.

d . Germanium Silicon and germanium form a mixed crystal in all proportions. In CZ silicon containing 3 x lo2' Ge atoms/cm3,new Orrelated LVMs at 11 18.5 and 1130 cm-I were observed at LHeT (Pajot, 1969; Newman, 1973). They were attributed to v3(Oi)perturbed by a Ge atom on a second neighbor site. Recent investigations by Yamada-Kaneta, Kaneta and Ogawa (1992) for Ge concentrations ranging from 6.5 x lo'* to 6.5 x lo2' atoms/ cm3have confirmed this point (Fig. 12). In this work, the same two modes were related to Oiperturbed by one Ge atom in two different sites, excluding the nearest neighbor of 0. The perturbation could also be observed in the Oicombination mode and on the 2DLFM. A conclusion drawn from these new results is that Ge alloying reduces the anharmonic coupling between v3 and the 2DLFM, and this causes a decrease of intensity of the combination mode resulting from this coupling with increasing Ge concentrations.

6.

SOME ATOMIC’ CONFIGURATIONS OF OXYGEN

217

IV. Quasi-Substitutional Oxygen I. SPECTROSCOPIES OF THE OXYGEN-VACANCY DEFECI

Irradiation of CZ silicon at room temperature with high-energy particles, for instance 2 MeV electrons, produces primary defects (vacancies, noted V , and Si, self-interstitials). These primary defects are mobile at this temperature, and they can recombine with each other. Vacancies can also combine with existing LDs. including other vacancies, to produce secondary defects that are stable at room temperature. The oxygenvacancy center ( A center or OV, used here for convenience) is formed when a nearest neighbor of the interstitial 0 atom is ejected. Formation of OV leads to a loss of 0, but a saturation in the production of OV occurs after electron doses of = S x 10’’ cm-’. This indicates a dynamic equilibrium between the trapping of V by 0; and the trapping of Si; by OV (Newman, 1973). OV can be seen as a vacancy in which one of the reconstructed bonds is “decorated” by an 0 atom. It can also be seen as a substitutional (unstable) 0 atom having undergone a (100) distortion that pushes this atom out of center with the breaking of the elongated bonds and the reconstruction of a Si-Si distorted bond (Fig. 13).The term suhsriturional oxygen is sometimes used for this defect by opposition to interstitial oxygen discussed in the preceding section. A difference between 0, and OV is that OV is electrically active. The origin of this activity can be depicted schematically by considering the reconstructed Si-Si bond, made up of two dangling bonds (atomic orbitals), having one bonding state filled by the two electrons and one empty antibonding state. The production of OV in n-type CZ silicon has shown that this antibonding state could trap an electron with an energy deeper than that of an electron binding on a group V dopants. This state was the cause of an acceptor level at E, - 0.17 eV reported by Wertheim (1957) and Hill (1959). The EPR spectrum (sometimes* labeled Si-BI) of this electron has been investigated in detail by Watkins and Corbett (1961). and they have shown that the extra electron density is shared by the Si atoms of the reconstructed bond. The neutral charge state OVo is diamagnetic, but optical excitation with = 1 . 1 eV photons can promote one electron from the bonding state into the antibonding state, producing spin one OVg=,, responsible for the Si-SI EPR spectrum (Brower. 1970 and 1972). An EPR spectrum (Si-I I ) observed also under white light illumination in n-type electron-irradiated C Z silicon has been tentatively ascribed to * W e follow the nomenclature where Si-BI means the EPR defect signature first obqerved in \ i k o n at Bell Telephone Laboratorie\. S o r SL stands for Sandia Laboratories. G for General Electric. etc.

218

B. PAJOT

FIG. 13. Model of a silicon unit cell containing an OV center. By comparison with Fig. I , the central atom has been removed and the 0 atom has rebonded to a second nearest neighbor. The four Si atoms nearest neighbors of V have been displaced inward to simulate relaxation.

OVf (Brosious, 1976). This last charge state could be produced by capture of a hole by OV!,, but no confirmation of this attribution has been reported so far. In OV, the 0 atom is bonded to two second nearest neighbor Si atoms. The stretching mode of this Si-0-Si structure gives LVMs at 836 and 798 cm-' for I60Voand of I80Vo,respectively (Corbett et al., 1961; Abou-el-Fotouh and Newman, 1974). The LVM of "OV- is shifted to 885 cm-' (Bean and Newman, 1971). The FWHPs of these LVMs are broad (=3 cm-') so that no Si-isotope effect is observed. The stress-induced splitting of the 836 c m - ' mode has been investigated (Bosomworth et al., 1970; Pajot et al., 1994). Figure 14 shows the splitting of this mode at 8 K for a 0.50 GPa stress along a [Olll axis. The results can be fitted to a center with a rhombohedra1 symmetry with a dipole along a ( 1 10) axis. The piezo-spectroscopic coefficients A , , A , and A , for OVo are respectively -2.4, 2.4 and 4.5 cm-IGPa-'. In samples with OV concentration much larger than the electron concentration available, Watkins and Corbett (1961) probed with EPR the energy-dependent redistribution of electrons among OV configurations with electronic energies shifted by a uniaxial stress applied at 77 K. They derived the stress-dependence of the electronic energy of OV- and, from the annealing of the effect, a thermalization energy of the electron from OV (0.20 eV) comparable to the position of the level given previously. For a stress along a (100) axis, they found a characteristic splitting of 42 meV.GPa-' for the electronic level. The atomic reorientation of the 0

6.

SOME ATOMIC CONFIGURATIONS OF OXYGEN

219

L--

825.0

$32 5

840.0

847.5

U A V I N L I M B L K (cni-1)

FIG. 14. Splitting of the OV" L V M in silicon at 8 K under a stress of 0.5 GPa along the [ I 101 direction. Polarization vector parallel to the stress (a) and parallel to [I101 (h). The bars show the positions of the three component\ and their relative intensities (Pajot el al.. 1994).

;itom of OV" was also measured after alignment with the stress applied at 125 K by probing again the reoriented fraction with the EPR of OV-. A reorientation energy of 0.38 eV was obtained and confirmed by IR dichroism recovery (Corbett et al.. 1961). Thermal emission of the electron trapped by OV can also be observed in DLTS as a single peak with an activation energy of 0.18 eV (Kimerling, 1977). Piezo-DLTS experiments on OV- have been made (Meese, Farmer and Lamp, 1984: Qin, Yao and Mou, 1984), and a splitting of the DLTS peak was observed. Their results have given an atomic reorientation energy of 0.38 eV and a stress-induced splitting of the electron acceptor level of 57 meV.GPa-' for mil( 100) that compare well with the values obtained from piezo-EPR and from piezo-absorption. A priori prediction of the distortion for an 0 atom placed in a substitutional site in a silicon crystal is difficult from cluster-type calculations including atomic relaxation with the modified neglect of diatomic overlap (MNDO) method. Apparently correct trends can arise from spurious effects related to the size of the cluster size and its SiH terminations (DeLeo, Fowler and Watkins, 1984). In the cih initio total-energy calculations by Ortega-Blake et al. (1989), a (Si,=Si)20, Si, cluster is used and the 0 atom and its four nearest neighbors are allowed to move. An off-center (100) distortion of 0.9 of the 0 atom and a reduction of the distance between the pairs of bonded Si atom are found that are supported qualitatively by experiment.

220

9. PAJOT

2. THERMAL STABILITY Watkins (1975) has observed in p - and n-type CZ silicon electronirradiated near 20 K an EPR spectrum (Si-G4) ascribed to a metastable OV-* center already present at 20 K. The conversion from Si-G4 to the Si-BI spectrum of the stable from OV- takes place near 100 and 45 K in p-type and n-type material, respectively. In this metastable OV-* center, the 0 atom undergoes a (100) distortion similar to the OV center stable at room temperature. In the p-type material, the annealing of the vacancies near 60 K produces another EPR spectrum (Si-G3) attributed also to a metastable OVI,;,, center that anneals near 90 K. In this last center, the 0 distortion is along a ( I 11) direction. On the high temperature side, the annealing of OV at 300°C produces a decrease of the EPR and 1R signals indicating an atomic modification or a dissociation of the defect. The loss of intensity of the OVo LVM is correlated with the growth of a new LVM at 889 cm-' at room temperature (Corbett et al., 1964b). These authors proposed that the new LVM could come from an 0,V center formed by the trapping by 0;of a mobile OV defect. This seemed to be substantiated by the quadratic dependence of the final intensity of the 889 cm-' LVM (896 cm-' at LHeT) on [Oil after complete annealing of OV (Lindstrom and Svensonn, 1986). A test for this interpretation is the 0 isotope effect of the LVM. Implantation in silicon of equal doses of I 6 0 and I8O producing directly I60V and "OV were performed by Stein (1986b). Annealing of the implanted samples at 300°C produced only the 889 cm-' LVM and its I 8 0 equivalent at 850 cm-'. No intermediate LVM was detected between these two modes. This point and the magnitude of the 0 isotope shift for the defect make unlikely the presence of two 0 atoms in this new defect (labeled A' center by Stein) unless these two atoms are weakly coupled. The A' center anneals out at -450°C and LVMs at 910,976,991 and 1005 cm-' (LHeT) are in turn observed in the samples. Because the annealing kinetics of the A' center is thermally activated with an energy of 2.6 eV, close to the activation energy for 0; diffusion (2.54 eV), it has been suggested by Lindstrom and Svensonn (1986) that these LVMs were related to 0; trapped near an A' center, but there is unfortunately no 0 isotope experiment here to tell how many 0 atoms are involved in this center. The above IR results on the annealing of OV should be compared to EPR studies on CZ silicon samples irradiated with high electron fluences near 100°C (Lee and Corbett, 1976). In these samples, two EPR spin-one spectra were attributed to 0-vacancies complexes: Si-A14 to OV, ( V , with a nearly substitutional 0 trapped on one of the V sites) and Si-P4

6.

SOME ATOMIC CONFIGURATIONS OF OXYGEN

22 1

ep. FIG. 15. Models for different polyvacuncy-oxygen complexes in silicon. The 0 atoms are represented as dotted circles and the dangling bonds as single-atom bonds: (a) OVq; th) O , V $ ; ( c ) OV:; ( d ) In 0,C‘T. not shown. the 0 atoms are 0’and 0”’of ( d ) (from Y . H . Lee and J . W . Corbett. (1976).P h y s . Re\,. B 13, 2653). The Si atoms labels are for EPR lines assignment and orbitals description not considered here.

to OV, (a nearly substitutional C ) trapped near one of the end vacancy of a V , chain along a ( I 10) axis). Models for these defects are shown in Fig. IS. From its production rate (0.05 center/electron.cm), OV, is assumed to be produced by a direct collision process, and it anneals out at about the same temperature as OV. It has been suggested (Davies et al., 1987b) that OV, could produce one of the aforementioned LVMs, observed at 991 c m - ’ after electron irradiation at 100°C. OV, is produced during the annealing of OV and OVz,and it anneals out in turn at -450°C. For these reasons, OV, could produce the LVM at 889 cm-’. Other EPR spin-one spectra observed after annealing are attributed to oxygen-vacancies complexes with more than one atom ( 0 , V 2 , OzV, and O,V,) when nearly substitutional 0 atoms get trapped near still “empty” vacancies (Lee and Corbett, 1976).

222

B. PAJOT

3. OTHER O-RELATED IRRADIATION DEFECTS a. Dejects with Interstitial Si

An LVM at 936 cm-' was first reported by Whan (1966) in n-type CZ silicon electron-irradiated at temperatures between 80 and 150 K, together with LVMs at 922,932 and 945 cm-'. Annealing sequences below 250 K under white light illumination or in the dark gave evidence of two charge states of the same defect, producing the LVM at 945 cm-I and a new one at 956 cm-'. The defects giving all the previous LVMs anneal out below 300 K except the defect giving the 936 cm-' LVM, which is stable up to 350 K. They were attributed to rather simple centers involving one defect and one 0 atom. The 936 cm-' LVM was also observed by Brelot (1973) who attributed it to Si,O, (an interstitial Si atom trapped The attribution was challenged by Lindstrom et al. (1984), who by Oi). found an annealing temperature near 300°C for this LVM observed after room temperature electron irradiation. New experiments by Stein (1989) show that if this LVM can also be produced by room temperature electron irradiation, it still anneals out at 350 K in agreement with the earliest results. A comparison of the creation rate of the related defect in C-doped and in C-free CZ silicon seems to support a SiiOi attribution and the experimental results can imply the existence of another LVM at the same frequency. b. Dejects with Carbon In C-containing CZ silicon, electron irradiation near ambient produces among other LVMs a set of five lines at 529,550,742,865 and 11 15 cm-' (LHeT), labeled C(3) that are related to the same center (Davies et al., 1985). C(3) is correlated with (i) an electronic line near 790 meV (C-line) observed at LHeT in photoluminescence (PL) or by transmission and (ii) with an EPR signature (Si-(315). Si-G15 has been correlated in turn with a hole trap at E, - 0.38 eV (Mooney et al., 1977). These are four manifestations of the same center assumed to be a CO complex. The C-line is due in absorption to the creation of an electron-hole pair (exciton) with the hole more tightly bound to the center than the electron (pseudo-donor) and in PL to the recombination of this exciton (Thonke, Watkins and Sauer, 1984). A vibronic structure is related with C-line: the local mode frequencies deduced from the position of the satellites are 528, 585, 1114 and 1172 cm-' (Wagner, Thonke, and Sauer, 1984) and the frequencies of two of them almost coincide with those of the LVMs measured by absorption. A C-isotope effect is observed only for the two high-frequency LVMs of the C(3) set and for the zero-phonon C-line

6.

SOME ATOMIC' CONFIGURATIONS OF OXYGEN

223

1'1 IOI'ON ENERGY (rnev) 789 8

15691

790 0

15690

WAVELENGTH (pm)

FIG. 16. C-isotope effect of the rero-phonon 790 meV line (here observed at LHeT by photoluminescence) in electron-irradiated CZ silicon. This line I S due to the recombination of an excilon bound to a C,O, complex ( K . Thonke. G. D. Watkins and R . Sauer (1984). Solid Sfare Commun. 51, 127).

(Fig. 16) while a weak O-isotope effect is found only in the PL spectra for the local modes at 528 and 585 c m - ' . This identifies the presence of C and 0 in the center. Stress splitting of the C-line indicated that the center had a low symmetry (CI)!).The presence of C, (interstitial carbon) in the center, deduced from a modeling of the radiation process (Davies et al., 1985) was confirmed by piezo-EPR studies by Trombetta and Watkins (1987), who also proposed a model of the center that met the symmetry requirements. However, the fact that the O-related LVMs are at much lower frequencies than the C-related LVMs was apparently not solved in this model. An ah initio cluster yields a model preserving the symmetry and accounting qualitatively for the frequencies observed (Jones and Oberg, 1992a). In this model, the presence of dangling bonds on three Si atoms frustrates the 0 atom as, whatever the Si pair bridged by 0, one of the dangling bonds is unsaturated. This dangling bond then tries also to form a bond with the 0 atom leading to a threefold coordinated

224

B. PAJOT

FIG.17. Proposed model for the CiO, complex in irradiated silicon shown embedded in a silicon unit cell. The 0 atom (small dark gray) and the C atom (medium gray) are threefold coordinated (R. Jones and S. Oberg (1992a). Phys. Rev. Lett. 68, 86).

0 atom (Fig. 17). The low frequency of the 0-related modes is due to the large Si-0 bond length (-1.85A) in this defect. An electronic line at 3942 cm-' (489 meV) is also observed by PL and in absorption in electron-irradiated CZ silicon (Davies et al., 1987a). The stress splitting shows that the related center has C,, symmetry. The 0and C-isotope sensitivity of the line indicates also that the related center (annealing out at 225°C) is also an (OC) complex, but no LVM has yet been correlated with this line. A strong argument for the presence of a vacancy in this center (COW has been given by Davies et al. (1987b). V. Comparison with Other Light Element Impurities 1. CARBON

The solubility of substitutional carbon in FZ silicon is -10I8 atoms/ cm3 near the melting point; it seems to be limited by the lattice shrinking due to the small atomic radius of C compared to Si. In CZ material, larger C solubilities can be achieved (-2 x 10I8 atoms/cm3) because carbon compensates the lattice expansion due to oxygen (Newman, 1986). The C atom sits on center, and it produces only one LVM at 608, 589 and 573 cm-l for 12C,13Cand I4C, respectively. The effective charge of C for this mode is q = 2.5 e. Due to a stronger coupling with the lattice, the anharmonicity of a substitutional atom is larger than that of an interstitial one and an overtone is observed at 1211 and 1175 cm-' for "C and 13C,

6.

225

SOME ATOMIC CONFIGURATIONSOF OXYGEN

respectively (Newman and Smith, 1969). C is isoelectronic to Si and electrically inactive. Interaction between C and 0 has been discussed in the preceding sections. C is not as reactive as 0, and only a few number of complexes with foreign atoms are known. With the group 111 acceptors, C can form acceptor complexes with an ionization energy -0.8 times smaller than that of the isolated acceptor. They have been investigated by several experimental techniques and also by extended Huckel calculations. The model that best fits the results is an acceptor surrounded by three Si and one C atoms (Jones et al., 1981). In C-containing silicon, electron irradiation below room temperature produces a characteristic EPR spectrum (G 12), attributed to a (100)-oriented C=Si interstitial defect (dumbbell) bonded to four Si atoms on regular sites (Watkins and Brower, 1976). This (CSi), defect is correlated with two LVMs at 922 and 932 cm-I (C(I) spectrum). I t anneals out at near ambient temperatures, and after an intermediate structure responsible for the C(2) IR mode, a new center is formed. It is responsible for a strong signal at 969 meV, observed by PL as well as in absorption (Fig. 18), and it can be used to detect carbon in FZ silicon with a better sensitivity (- IOl4 atoms/ cm') than by measuring the substitutional C LVM (Davies et al., 1984). A S = '/z EPR spectrum (GI I ) is related to this new center in the positive charge state, and it was identified by Brower (1978) as two nearsubstitutional asymmetric C atoms separated by an interstitial Si CC,Si,C,J. The C isotope effect of the vibronic sidebands of the 969 meV line gives evidence for the presence of only one C atom in the center

1

I

+

d

I L

1

~

96975

9695

96925

I'IiOTON ENERGY (mev)

FIG. 18. Absorption at 2 K due t o the 969 meV line in a nominally C-free and 0-free silicon sample irradiated with 5.6 x 2 MeV electronsicm!. That line is due to a C,Si,C, complex produced by the irradiation. IC) is estimated to be 2 x atoms/cm3. The IR path is 20 mm (G. Davies, R . Lightowlers. M . C. do Carmo. J . G . Wilkes and G . R . Wolstenholme (1984). Solid Stare Comrnrrn. 50, 1057).

226

B. PAJOT

(Davies, Lightowlers and do Carmo, 1983). This puzzle was solved by the ODMR observation of a S = 1 excited state of the neutral center (O’Donnel, Lee and Watkins, 1983). In this configuration, the structure of the excited neutral center at low temperatures would be somewhat similar to that of 0; when replacing the two equivalent Si atoms by two C atoms and the 0 atom by Si. Unfortunately, no LVM related to this center has been reported. 2. NITROGEN The solubility on nitrogen in silicon is much lower than that of carbon and [N] - 1015 atoms/cm3 in bulk-doped crystals is a representative figure. N doping is achieved by CZ growth in N, + Ar atmosphere or by adding Si3N4to the polysilicon charge prior to melting. O-free, but Ndoped Si has also been obtained by CZ pulling from a silicon nitride crucible (Watanabe et al., 1981). For research purposes, N implantation whether followed or not by annealing is also used, and in that case, N concentrations 1020 atoms/cm3 can be achieved by laser annealing (Stein, 1986a) as nitrogen solubility increases with the growth velocity of the solid phase. N is not a shallow dopant like the other group V elements, and this is related to its small atomic radius that seems to preclude an on-center substitutional location.

-

a. Isolated Nitrogen

In N-implanted laser-annealed silicon, an EPR spectrum (SL5) is observed to be stable up to 400°C, where it is replaced by SL6 and SL7 (Brower, 1982). These paramagnetic centers account only for a small ) the total N present. SL5 is attributed to a substitufraction ( ~ 0 . 0 5 - 0 . 1of tional off-center N atom with a (1 1 1 ) distortion. The hyperfine (hf) interaction indicates that the fifth electron is localized on one of the four surrounding Si atoms. The small reorientation energy of N among the four equivalent sites (=O. 107 eV) was interpreted by a location of the N atom near the center of rotation. This point was clarified by Murakami, Kuribayashi and Masuda (1988) who observed that the hyperfine splitting of SL5 increased with temperature from 150 K. They interpreted this fact by the existence of an on-center metastable minimum of the N atom intermediate between off-centers stable (1 1 1 ) locations. The observation conditions of SL5 are the same as those of a N-related LVM at 653/637 cm-l ( 14N/”N) reported by Stein (1985). Hence this LVM is attributed to off-center substitutional N . The comparison with the 14C LVM (573 cm-’) indicate an average bonding stronger between Si and N than between Si and C. From DLTS measurements (Tokumaru et al., 1982), a

6.

--.

227

SOME ATOMIC (‘ONFIGURATIONSOF O X Y G E N ~

“ ~ - 1 . 5 ~

T

-

f

A

’*N/crn’.

*

1

B=’5N/cm’

.

7 irN-~5N

B / A = 1 .O

crl

z E/A=O 5

0, E/A=0.2

I SI-N PAIRS FOR DIFFERENT ” N / l 4 N AABS.=O.Ol AFTER LASER ANNEALING

RATIO T_=80

700

770

840

1

I

9 10

980

WAVENUMBER (cm-1) FIG. 19. Absorption at 80 K after laser annealing of silicon implanted with overlapping profiles of I4N and ”N with different ”N/I4N ratios ( H . J . Stein (1986a). M a t . Res. S y m p . Proc. 59, 5 2 3 ) .

value of 0.3 e V seems to be the most probable for the position of the deep level associated with SLS. Total energy Hartree-Fock calculations by Hjalmarson and Jennison ( 198s) show that a trigonal distortion of the N atom in the preceding structure spontaneously occurs when the four surrounding Si atoms relax either outward or inward, but that the inward relaxation is more likely. PI, lines investigated in silicon samples containing C and N isotopes have been convincingly attributed to some kind of interstitial distorted CN pair due to the pairing of C with off-center N (Dornen. Sauer and Pensl, 1986). However, no CN-related LVM has been observed in samples where they could have been present (Stein, 1988). h. The Nitrogeri Pairs Two “N-related LVMs were observed at 747 and 963 c m - ’ at ambient temperatures in N-doped silicon (Abe et al., 1981) and also in implanted material (Stein. 1983). The comparison of I4N-implanted and I5N implanted samples with a I4N-’’N coimplanted sample by (Stein, 1986a) indicated an interaction between N atoms in the related centers because of the occurrence of an intermediate 14N-”N LVM (Fig., 19). Existence of N-N pairs bonded to Si atoms were then suggested to be responsible for the two LVMs. These pairs are stable up to 6 W C , but in samples

228

B. PAJOT

coimplanted with 0 (Stein, 1988) or taken from N-doped CZ crystal (Qi et al., 19911, new LVMs at 805-810, 1000, 1030 and 1064 cm-' are observed after laser annealing. They can be attributed to perturbation of the vibration of the N-N pairs by Oiand also to the inverse. From the intensities of the LVMs, the N pairs must be the most abundant N-related species in silicon. c'.

N-Related Shallow Donors vs. Thermal Donors

An N-related PL line at 1122 meV has been reported in N-doped silicon as well as the presence of a small concentration of N-related shallow donors with concentrations - 0 5 1 . 3 % of the total [N] (Tajima et al., 1981). It is not clear if these two observations are related and if the PL line does or does not come from excitons bound to the N-related shallow donors. Shallow donors ascribed to nitrogen-oxygen complexes have also been reported by Suezawa et al. (1986; 1988), who observed in Ndoped CZ silicon hydrogenlike spectra of seven centers with ionization energies ranging from 32.6 to 37.4 meV. Some of these centers were as-grown with a rather high stability compared with the 450°C TDs, and others were produced by annealing near 450-500°C. It has been suggested from a kinetic analysis that one of these complexes contains two pairs of N atoms and another three pairs. It is likely that some of these centers were also among the ones reported by Navarro et al. (1986) using photothermal ionization spectroscopy (PTIS) on supposed N-free CZ Si. This raises the case of nitrogen as a low-background residual impurity in silicon (a very small amount of oxygen-nitrogen complexes could be detected by PTIS). The same question is raised by the observation by Hara, Hirai and Ohsawa (1990) in N-doped Si samples after long annealing at 470°C of an EPR spectrum identified as NLlO (Muller et al., 1978), not present in the N-free samples. In this case, it seems that the presence of N in NLlO can be ruled out (Ammerlaan, private communication) so that the case is still open. The presence of C in the N-doped CZ samples modify the kinetics of formation of the previous shallow donors and other shallow donors are formed (Hara and Ohsawa, 1991) but experiments providing direct evidence of N in these shallow centers are still needed. 3. HYDROGEN

Hydrogen is introduced in bulk undoped silicon by FZ growth under a H, atmosphere and bonded H atoms are detected from the absorption of the SiH LVMs (Bai et al., 1985). The concentration of bonded H in the undoped material is difficult to estimate. A comparison with germanium (Haller, 1991) gives [HI = 1-3 x IOl4 atoms/cm3. The two strongest

6.

S O M E ATOM'( (ONFIGURATIONS OF OXYGEN

2220.0

2222.5

229

2225.0

W A V E N U M B E R (cm-1) Fib. 20. Si-H stretching mode at h K i n a vacancy "decorated" by four H atoms i n FZ silicon grown in a H, atmosphere t U . Cleriaud (1991). Phvsicrr B 170, 383). The relative intensities of the lines match the relative abundances of the Si isotopes.

L V M s in the as-grown material at 1952 and 2223 c m - ' have a fine structure characteristic of a Si-H bond (Fig. 20). The intensity of the L V M at 1953 c m - ' is correlated with that of two L V M s at 794 and 814 c m - ' (Pearton. Corbett and Shi. 19x7). On the other hand, H/D doping shows that only one H atom is related to the 1952 c m - L V M . So, the 794 or the 814 c m - ' L V M could be due to the wag mode and the 1952 c m - ' L V M to the corresponding stretch mode. The presence of a second lowfrequency mode could indicate a defect with two weakly coupled H atoms. The attribution of the 1,223 c m - ' L V M to a tetrahedral center with four H atoms (Bai et al., 1985) was confirmed from stress-splitting measurements by Bech Nielsen, Olajos and Grimmeiss (1989), who suggested a hydrogen-decorated vacancy VH4. The calculations predict that the most stable configuration for H and H" is the interstitial BC location where H is midway between two Si nearest neighbors. This produces a large outward relaxation of the two Si atom (-0.4 A), but it is compenu t e d by the energy gained in forming a Si . . . H . . . Si three-center bond (Van de Walle, 1991). This structure is reminiscent of O;, but the

230

B. PAJOT

bonding is different. BC Ho is paramagnetic and the AA9 EPR spectrum has been attributed to this center (Gorelkinskii and Nevinnyi, 1987). To obviate the low solubility of hydrogen in pure silicon, proton implantation has been used for a long time to study H-related defects (Stein, 1979). The presence in the implanted material of H-related defects is inferred from the many LVMs in the 2000 cm-’ region (see Pearton et al. (1987) for a list). The symmetry of some of these centers has been determined from the stress splitting of the LVMs and they seem to be related to vacancy- or divacancy-like centers “decorated” with one or more H atoms (Bech Nielsen and Grimmeiss, 1989). In H-implanted CZ silicon, LVMs at 870 and 891 cm-’ attributed to the vibration of 0 in an OV center decorated with H atoms (OVH, and to OVH-) have been reported (Mukashev et al., 1991). Configurations and electrical activities of the OVH, and OVH centers mentioned earlier have been calculated by cluster MNDO and Xa-DV methods (Gutsev et al., 1989). A structure with a chemical OH bond is obtained for O W ; for OVH,, the two H atoms bond to the broken Si-Si reconstructed bond of OV. Surprisingly, the O W , center is found to have a deep level in the gap so that it could not be said that hydrogen passivates OV. An electrical manifestation of the interaction between hydrogen and shallow dopants in silicon is their neutralization (see Johnson et al. (1991) for a review). The idea that hydrogen could interact with acceptors to form electrically neutral pairs was confirmed by the results by Pankove et al. (1985) and Johnson (1985): in B-doped silicon neutralized by hydrogen, they reported the existence of a LVM at 1870 cm-’ (ambient) that they attributed to the stretching mode of a BH complex. The existence of H-related LVMs with A1 and Ga acceptors was shown by Stavola et al. (1987). These complexes were formed in p-type material by Coulomb attraction between a proton (an H atom having captured a hole) and a negative acceptor ion. The difference with Li, which behaves similarly (Chrenko et al., 1965), is that instead of an atom pair stabilized by electrostatic interaction, a chemical bond is formed in the case of hydrogen. The solubility of hydrogen in p-type silicon in the form of acceptorhydrogen complexes has been studied mainly for the B acceptor, where it follows roughly the B concentration. [BH] lozocenters/cm3 on 3 k m beneath the hydrogenated surface have been reported by Herrero, Stutzmann and Breitschwerdt (1991). In these complexes, H is in a BC location along the (1 1 1 ) direction between B and one nearest neighbor Si atom (Fig. 21a). The main bond is between H and the Si atom (the stretching frequency is too low for a B-H mode), but a weak bonding exist also between H and the B atom, demonstrated by the existence of a small

-

6.

SOME ATOMIC C O N F I G U R A T I O N SOF O X Y G E N

23 1

FIG.21. Representation of a silicon unit cell with (a) an acceptor-hydrogen complex. The relaxation shown is approximately the one for the B acceptor (dark gray). The H atom is shown in black. 'The same cell with ( h ) a donor-hydrogen complex. The relaxation of the donor atom (dark gray) is small compared with that of the Si atom bonded t o H.

B-isotope effect of the Si-H . . . B L V M (Pajot et al., 1988).The reasons why a Si-H bond is formed instead of a B-H bond lie in the fact that, in this center, the atoms keep their natural coordination. The properties of the model calculated by DeLeo and Fowler (1985)agree with the experiments, and they predict a reasonable value of the stretching frequency

232

B. PAJOT

of the Si-H . A1 LVM. No wag mode of these complexes has been observed, perhaps because of the small displacement of the H atom in the (1 11) plane or of the low-frequency of this motion. Substitutional B in silicon reduces the average lattice spacing of the crystal as the tetrahedral B radius is smaller than that of Si. The formation of a BH complex relaxes partially the stress because it increases the distance between unbonded atoms (Herrero et al., 1991). A1 and Ga atoms have atomic radii equal to or larger than that of Si. At LHeT, only one line is observed for the LVMs of BH, AlH and GaH complexes, but above -40 K, a low-energy satellite appears for the AlH and GaH complexes (Stavola et al,, 1987). By analogy with the situation for Oi this can be an indication that in these complexes, the Si-H bond direction makes an angle with the (111) axis. The question of the respective stabilities of the BC and off-axis location of H in the acceptor-hydrogen complexes has been addressed by Amore Bonapasta, Giannozi and Capizzi (1992). The stress splitting of the LVM of the BH complex is consistent with a trigonal symmetry when measured by IR absorption at I5 K (Bergman et al., 1988b) in agreement with the preceding model, and a Si-H bond reorientation energy of 0.2 eV is measured (Stavola et al., 1988)that is the same as the one predicted (Van de Walle, 1991). However, the off-axis displacement of the H atom is relatively easy. For this reason and to explain piezo-Raman results at 100 K on the Si-H . B LVM, one has to assume that a (1 11) stress applied at 100 K can distort the Si-H bond out from the (111) axis (Herrero et al., 1991). The effect of a stress along the (1 11) axis of the acceptor-hydrogen complexes on the direction of the Si-H bond has been modeled by Estreicher, Throckmorton and Marynick (1989) using cluster calculations, and they point out the influence of the acceptor-hydrogen coupling with increasing stress. The results of channelling experiments at 30 K on the BH complexes are consistent with a BC location of H (Bech Nielsen et al., 1988). Deicher et al. (1991) present a review of the results on the location of H in BH and InH complexes using nuclear techniques. In n-type silicon, H can also form complexes that neutralize the donors (Johnson, Herring and Chadi, 1986) but neutralization is not as efficient as for acceptors. LVMs associated with the donor-hydrogen complexes indicate that the H atom is not bonded to the donor atom, but to one of the nearest neighbors Si, Bergman et al. (1988a), in agreement with the prediction of Johnson et al. (1986). Unlike the acceptor complexes, the H atom is interstitial along a (111) antibonding direction symmetric to the BC location just discussed (Fig. 21b). The frequency of the stretch mode of these Si-H bonds is near 1560 cm-' at LHeT, significantly lower than the ones in the acceptor complexes, because the antibonded H atom is not constrained by another atom as in the BC location so that its bond

-

6.

233

SOME ATOMIC CONFIGURATIONS OF O X Y G E N

FIG.22, Model of the double donor-hydrogen complex (S and H atoms shown dark gray and black) (after A . S . Yapsir. P. Derik. R . K. Singh, L. C. Snyder, J . W . Corbett and T.-M. Lu (1988). Phys. R e v . B 38, 9936). This configuration should be the same for the di-hydrogenated OV center.

length must be slightly longer. For the same reason, this Si-H bond has also a wag mode near 810 c m - ’ . Another LVM is observed about 100 c m - above the Si-H stretching mode, and there is no clear attribution for this mode (Bergman et al., 1988a). The stress-induced splitting of the As. Si-H stretching mode is consistent with a trigonal symmetry of the center (Bergman et al., 1988b). Recent cluster calculations on the P , Si-H centers confirm the location of H antibonded to Si while Si relaxes out from P by -0.6 A so that the Si-P bond can be considered broken (Denteneer et al., 1990). The frequencies calculated by these authors (stretch: 1460 c m - ’ and wag: 740 cm ‘ ) show a substantial improvement on preceding results (see for instance Stavola (1991) for a comparison). Hydrogen neutralization of S , Se and Te double donors measured by DLTS has been reported by Pens1 et al. ( 1988) and this surely means the binding of two H atoms in the vicinity of the chalcogen donor (Fig. 22). The same structure as this one is predicted by Yapsir et al. (1988) for an OVHz center.

’

VI. Oxygen in Other Semiconductors

I . GERMANIUM

Oxygen is not a residual impurity in germanium. Different methods have been used to dope this material with oxygen (maximum 101 7 x 10” atomsicm’) and 0-related absorptions have been reported (Bloem,

-

234

B. PAJOT

Haas and Penning, 1959; Kaiser, 1962; Stein, 1973). A LVM at 862 cm-' (LHeT) is observed that shift at 818 cm-' with IgO (Whan, 1965). It is attributed to the u3 mode of Ge-0-Ge (OJ.Another LVM has been reported near 1270 cm-' (LHeT) with an intensity proportional to that of u3 (Kaiser, 1962). 0-related TDs are also produced in germanium by annealing near 350°C and the relative Oi loss seems to be more important than in silicon while annealing at T > 600°C leads to the precipitation of GeO, (Kaiser, 1962). The TDs in germanium are double donors as in silicon; the energy of their electronic spectrum is shifted to lower energies with respect to silicon, as for all the hydrogenic spectra that can be observed in both semiconductors (Clauws and Vennick, 1984). By analogy with the Si isotope splitting of v 3 in silicon, 15 isotopic components are expected from the Ge-isotope effect for that mode in germanium in a spectral interval of about three wavenumbers (the percent of natural abundances of the Ge isotopes are 'OGe: 20.50, '*Ge: 27.40, 73Geand 76Ge:7.80, 74Ge:36.50). The average FWHP of the components of u3 in germanium is -0.04 cm-' (Pajot and Clauws, 1987), and they should be fully resolved under high resolution. The number of components actually observed at 6 K under high resolution is larger, and it indicates that transitions from thermalized levels already occur at this temperature (Fig. 23). For each isotopic combination, three components labeled L(ow), C(entra1) and H(igh) can be seen at 6 K using standard germanium material. The H-C and C-L separations are -0.067 and 0.229 cm- I , respectively. In monoisotopic germanium (74Ge),where extra components are due only to thermalized levels, a fourth low-energy transition, (N), distant of C by 0.48 cm-' has also been observed at LHeT, as shown in the inset of Fig. 23 (Khirunenko et al., 1990). The fit of the isotope shift used for Oiin silicon (Pajot and Cales, 1986) when repeated for germanium gives a value of the apex angle Ge-0-Ge of 140" and an interaction mass M' of 11.65 amu. As for silicon, it is found that the Ge-0-Ge angle is larger in the elemental material than in the oxide (Pantelides and Harrison, 1976). In germanium, the distance between Oi and the ( 1 1 1 ) axis is 0.6 A compared to 0.2 A in silicon, and this results in smaller energies related to the hindered rotation or tunnelling of the 0 atom. In the free-rotator approximation, the first excited level would be at 3.2 cm-I. Phonon spectroscopy, briefly described in the section on 0; in silicon, has provided spectacular results in the case of Oi in germanium (Gienger, Glaser and Lassman, 1993). Figure 24 shows the phonon spectrum of Oiin germanium at I K. At zero stress, above the 1.2 meV (9.7 cm- ') onset of Sn-insulator-Sn detector, eight transitions are observed between -10 and 22 cm-'. An analysis of the results shows that even at 1 K some of the transitions already arise from thermalized levels as the

6.

235

SOME ATOMIC'CONFIGURATIONS OF O X Y G E N

864.4

8634

862.4

861.4

860.4

WAVENl JMBEK (cm-1) Fic. 23. Absorption of v,(''O,) in germanium at 6 K. The fine structure is due to the Ge isotope effect and the thermalization of the first levels (Pajot, 1990). By comparison. a ~monoisotopic 0,) 74Ge(inset) shows only the fundamental and LHeT spectrum of ~ ~ ( 'in lhermalired components for ''Ge20 (L. I . Khirunenko, V. I. Shakovstov, V . K. Shinkarenko and F. M . Voroblako (1990). F k . Tekh. P o l u p r o r d n . 24, 1401: Sov. Phvs. Semiw n d . 24, 663). The asterisks denote the contribution of the components C , H and L of the inset.

/

c

0 , 2x1017~m-3 PI1 I l l O l

OMPo

J

c f

-

D

I

1

2

3

PHONON E N E K ( i Y (meV) Fici. 24. Phonon absorption spectrum at 1 K of 0, in germanium as a function of a (110) stress. Some of the lines arise from already thernialized sublevels. The transitions with the lowest energies cannot be observed because of the experimental cut-off at 9.3 c m I~. At bottom right are shown the Al-insulator-Al phonon generator and Sn-insulator-Sn detector evaporated on the sides of the Ge sample (Gienger et al., 1 9 3 ) .

236

B. PAJOT

first two excited levels are 1.45 and 5.40 cm-' above the 0 K ground state. The free-rotator analysis cannot account for such low energies, and it seems that in germanium, the lower value of 2a does not allow nearly free rotation as in silicon, but only hindered rotation. The potential barrier between the six equivalent minima about the ( 1 11) axis allows tunnelling between these minima that produces a splitting of the levels depending of the barrier height (Hrostowski and Alder, 1960). The stress-induced dichroism of Oiin germanium was also observed and the results are qualitatively the same as for silicon (Corbett et al., 1964a). The reorientation energy of Oiis smaller in germanium (2.08 eV), where the diffusion of 0 is thermally activated with a preexponential term Do = 0.40 cm2/s at room temperature. This means that in germanium 0; is mobile at a lower temperature than in silicon. Irradiation of l60/I80-dopedn-type Ge at 25 K does not produce new LVMs, but after annealing at 73 K, a LVM at 719/683 cm-' (160/'80) appears. The associated center contains only one 0 atom and it anneals out near 160 K. A new center is created with a LVM at 620/589 cm-' (160/180) containing also one 0 atom (Whan, 1965). The similarity in stability between this center and the one giving an EPR spectrum attributed to OV- (Baldwin, 1965) suggests that the 620 cm-' LVM is associated with OV- in germanium. Near 373 K, this center seems to transform into new ones producing LVMs at 808 and 715 cm-' ("0).A strong LVM at 780 cm-' (I6O)appears after annealing above 373 K and isotopic substitution with I8O shows that the associated center contains two 0 atoms. These annealing sequences are reminiscent of the ones for OV in silicon, but in germanium, much less EPR data are available so that information on the symmetry of the centers produced is scarce. A study of the annealing of O-doped n-type germanium irradiated with y-rays seems to show that the O p / O V - level is at E, - 0.27 eV (Litvinov, Urenev and Shershel', 1983). 2. GALLIUM ARSENIDE a . Interstitial Oxygen and OVA, It has been thought for some time that semi-insulating (SI) gallium arsenide (GaAs) could be obtained by doping with oxygen, hence the interest for the properties of this element in GaAs. Several doping techniques were then used like a partial pressure of O2 or the addition of Ga,O, or As,O, in the starting material (see Martin and Makram-Ebeid (1986) for a review). The maximum solubility of oxygen in GaAs measured by charged particles analysis (CPA) seems to be in the range of l x 10l6 atoms/cm3 (Shikano, Kobayashi and Miyazawa, 1985). The first

6.

SOME ATOMIC' CONFIGURATIONS OF OXYGi5.N

237

report by Akkerman. Borisova and Kravchenko (1976) of an 0-related LVM attributed to v3 of 0;at 8361790 cm- I ( 'hO/'XO)in GaAs doped with "0 enriched As@, went unnoticed for some years. Song et al. (1987) reported the observation in GaAs Si of photo-sensitive LVMs at 715 and 731 c m - ' they attributed to the deep defect EL2 but they recognized afterward (Zhong et al.. 1988) that these LVMs were due to an oxygenAs vacancy center ( O V A , ) . This point was confirmed by Schneider et al. (1989) using "0-enriched samples. This is a change with silicon and germanium as in GaAs, OVA,is a native defect. This is due to the fact that GaAs is a compound semiconductor where vacancies of both types can exist due to small differences to the exact stoichiometry. By analogy with silicon and in germanium, interstitial oxygen in GaAs is expected to be bonded to nearest neighbors As and Ga atoms. The vj mode must then be a doublet due to the Ga isotopes ("Ga: 60%, "Ga: 40%). This doublet (845.44 and 845.82 c m - ' at LHeT) was indeed reported by Schneider et al. (1989) and Song et al. (1990a), and it is shifted by 44 cm-l when '('0is replaced by "0. This frequency is not too different from the one reported earlier for 0, in germanium. In samples with low internal strains, the FWHP of the u3 isotopic components is 0.06 cm-I at LHeT (Song, 1992). Unlike germanium, there is no thermalized component at LHeT (shown later in Fig. 26b). The temperature broadening of the mode is rapid and barely detectable at 77K. The bonding of 0 to a Ga atom and to an antisite AsGa second nearest neighbor near VA, would also produce a doublet. However, the stress-induced splitting of u 3 shows that the dipole is oriented along (1 1 1 ) whereas Ga-0-As,, would have a ( 1 10) symmetry (Song et al., 1990b). There is no reason for 0 to be midway between As and Ga, and some asymmetry can be inferred from the absence of internal rotation about the ( I I I ) axis. An ub initio calculation finds that the 0 atom is nearer from t h e Ga atom (1.59 A) than from the As atom (1.88 A ) for a Ga-0-As apex angle of 158" and that the displacement of the As atom is very small (Jones and Oberg, 199%). The agreement between the predicted frequencies and the ones for h9Ga'60As/69Gai80As compared observed is fair: (924/875 cm An effective charge of 2.1 e is also obtained for uj to (846/802 cm-')c,bs,. and this value yields a maximum lo,]of 3 x 10"atoms/cm3 in the samples investigated. The calculation predicts another mode at 302 cm- but this frequency is located in the one-phonon strong absorption region of GaAs, and its observation would be very difficult. The stress splitting amplitude of v 3 is comparable to the one in silicon, but easier to measure because of the smaller FWHP in GaAs (Fig. 25). In GaAs, reorientation of 0, (Fig. 26a) is observed when cooling the sample under stress from room temperature (Song, 1992) whereas starting ~

238

B. PAJOT

.2

c

846.0

-1

845.2 0

F / l [OOII

0

TlT TI/

7 50

-_--100

150

STRESS (MPa) FIG.25. Splitting of ~ ~ ( in 0 GaAs , ) at 8 K as a function of a [I101 stress with a [OOI] viewing axis (C. Song, B. Pajot, and C . Porte (1990). Phys. Rev. B 41, 12330). H and L correspond to "GaOAs and 69GaOAs,respectively.

temperatures above 300°C are required for Oiin silicon and germanium (Corbett et al., 1964a). The reorientation energy of Oiin GaAs is between 0.8 and 1.1 eV, but it is not possible to know from the spectroscopic data whether the reorientation takes place about the As atom or the Ga atom. The dissociation energy for a diatomic Ga-0 molecule is 285 kJ/mole compared to 481 kJ/mole for As-0, but the cluster calculation of Jones and Oberg (1992b) indicate an inverse trend: they deduce a reorientation energy of 0.5 eV about the Ga atom (breaking of an As-0 bond) and of 1.84 eV about the As atom (breaking of a Ga-0 bond). Hence, actual reorientation must take place preferentially about the Ga atom. For this reason, care must be exercised when deducing an Oi diffusion coefficient from the experimental reorientation energy. In GaAs, three LVMs labeled A , B and C (italics are used to avoid confusion with chemical symbols) are attributed to different charge states of OVA,. The primary attribution comes from the observation of three components for each of these LVMs (Fig. 27). These components are

6.

SOME ATOMIC CONFIGURATIONS OF OXYGEN

239

due to the Ga-isotope effect, and they indicate that an 0 atom is symmetrically bonded to two Ga atoms. The simplest defect rendering this bonding possible is an As vacancy, hence the attribution. Two of the LVMs are observed under thermal equilibrium: mode A near 731 cm.-' corresponding to the most positive state is observed in Sl GaAs and mode B near 715 c m - ' in n-type material. In weakly n-type material, both modes are observed (Alt, 1989a; Song, Pajot and Gendron, 1990a). After a short illumination of S1 GaAs at LHeT with photons in the 1.25 eV range (-- 1 pm), a third mode, labeled C (Song et al., 1990a) or B" (Alt, 198Yb), can be observed to grow near 714 cm. at the expense of A (Fig. 27). In the S1 samples where EL2 and OVA,are both present, interconversion of A can occur under illumination with photons in the 1.25 eV range. Figure

'

WAVENUMBER (cm-1)

.

'

ldl i

WAVENUMBER (cm-1) 2h. (a) Stress-induced dichroism of ~ ~ ( 'in" GaAs 0 ~ )at 8 K due to atomic reorientation under a I101 stress of 120 MPd. Elland E , indicate the polarization directions parallel or perpendicular to the aligning stress. (b) Polarized reference spectrum of ~ ~ ( 'in~GaAs 0,) at 8 K of an unstressed sample showing n o dichroism. The Ell spectrum is shifted by 0. I c m - ' for clarity (Song. 1992). FIG.

240

B. PAJOT

0.40

0.32

z 0.24

2 0.16

0.08

0 .oo

73i.7

71

WAVENUMBER (cm-1) FIG.27. Modes A , B and C of I60VAsinGaAs at 6 K. H H , H L and L L stand for 71Ga10, 7'Ga069Gaand 69Ga,0, respectively (Song et al., 1992).

ILLUMINATION TIME (s) FIG.28. Change under illumination with 1.25 e V photons at 6 K of the concentration of the different charge states of OVA,in SI GaAs represented by the intensity changes of the corresponding LVMs (the component with two "light" Ga isotopes ( L L ) is used) (Song et al.. 1992).

28 shows the charge transfer from A to B followed by the inverse. The fast transfer from A to B is explained by the photoionization of EL2' in the conduction band and by the preferential trapping of the photoelectrons by OV,,. The second part of the interconversion is mediated by the photoionization of EL2' in the valence band. This photoionization

6.

S O M E ATOMIC' CONFIGURATIONS OF OXYGEN

24 1

produces holes in the valence band and their recombination with EL2" competes with the phototransfer of EL2" into the metastable state by photons within the same energy range (Martin and Makram-Ebeid, 1986). The metastable state of EL? is electrically inactive so that the holes left are available for trapping by negative OVA,( B )that returns to the positive state ( A ) . The two peaks of observation of C show that this mode must correspond to an intermediate state between those giving A and B. Hence, there is a charge difference of two between the stable states producing A and B and this i s characteristic of a center with negative ( J (Alt, 1990; Skowronski, Neild and Kremer, 1990). The charge states corresponding to A , B and C' are attributed to OV:,, OV:; and OVA,, respectively. The position in the gap of the levels associated with OV;; and with OV,,, ( E , - 0.6 eV and E, - 0.14 eV, respectively) has been determined from the intensity decrease under annealing of modes B or C created by illumination (Ah, 1990; Skowronski et al., 1990). In n-type 0-containing GaAs, several electron traps have been detected including EL2 and EL3. The similitude between the energy signature of EL3 and that of OV;; leads to ascribe electron trap EL3 to OVA,(Kaufmann et al.. 1991; Neild, Skrowronski and Lagowski, 1991). There is an uncertainty on the absolute charge state of OV in SI GaAs and the ab initio calculations of Jones and Oberg (1992b) predict that the charge state should be OV,, instead of OVX, so that all the charge states should be shifted. None the less, with these attributions, at least one of the OVA, states is paramagnetic, but no related EPR spectrum has been detected u p to now. This can be due to the large widths of the EPR lines in GaAs that require a rather large concentration of centers. The splitting of A , B and C' under stress is consistent with a dipole oriented along a ( I 10) axis and this confirms the structure of the center (Song, 1992). The splittings for A and B are similar and this seems to indicate that the relaxations of the corresponding charge states are comparable while the relaxation for OV?,; should differ. The atomic reorientation of OVA,follows qualitatively the one of OV in silicon; in particular, no dichroism is detected for a stress parallel to [ I101 applied from room temperature when the propagation vector of the radiation is along [0011 (Pajot et al., 1994). In samples containing OV;, and Ova;, a stress applied from ambient produces electronic reorientation and the formation of OVA,without illumination. This fact can be attributed to the trapping of a single electron by OV;,. OV,, is normally unstable above -95 K . but it is assumed that the stress stabilizes this charge state and allows its observation (Song et al., 1992). The annealing of OVA, between 650 and 750°C results in an increase of the 0,concentration (Skowronski and Kremer, 1991). Short-term anneal-

242

B. PAJOl

ing near 1200°C produces new 0-related LVMs that can coexist with the OVA, LVMs (Skowronski, 1992). The fine structure of these new LVMs resembles that of the OVA, modes. One near 733 cm-' is a triplet indicating again an 0 atom bonded symmetrically to two Ga atoms. Two other ones, close in frequency are quadruplets. The extra line results from the splitting of the "Ga0"Ga component (HL in Fig. 27) and this indicates that the two Ga atoms bonded to oxygen are no longer equivalent. Tentative models for these new centers have been proposed by Skowronski (1992). In 0-containing samples, a LVM near 604 cm-' is observed (Song et al., 1990a; Skowronski and Kremer, 1991). The triplet structure indicates a Ga-X-Ga structure for the center. No measurement on I80-enriched samples has been made (an I8O mode would be expected near 570 cm-'1. The frequency of this mode is comparable to the one reported by Whan (1965) for a center attributed to OV in germanium. This center is different from the one giving modes A , B and C as it is insensitive to near IR illumination. A possible attribution would be a Ga-0-Ga structure in an environment different from the previously discussed OVA, center. Carbon does not seem to be directly or indirectly involved in the 604 cm-' mode, as it is observed also in the Bridgman samples with a very low C concentration. Other LVM have been observed in 0-containing S1 GaAs (Song et al., 1990a; Skowronski and Kremer, 1991) but information on their structure is too scarce for a reasonable discussion on their origin. In short-term rapid thermal annealing (RTA), the A mode and the 604 cm-' LVM starts decreasing in intensity at -600°C with a correlated increase of the intensity of v,(O,), and these native centers seem more stable than OV in silicon. Long-term annealing indicates the formation of other 0-related centers and finally the precipitation of oxygen (Skowronski and Kremer, 1991). b. OH-Reluted Centers

In some 0-containing GaAs, high-frequency LVMs are observed between 2900 and 3500 cm-' (Pajot and Song, 1992a). Such frequencies imply the stretching of a NH or of an OH bond. The strongest of these LVMs (3300 cm-' at LHeT with a FWHP of 0.13 cm-') has a weak satellite at 3298.54 cm-I with a relative intensity of 0.03 (Fig. 29). The calculated frequency and the relative intensity of an "OH oscillator mode compared to 160H at 3300 cm-' are respectively 3298.14 cm-' and 0.037. For these reasons and because SI GaAs is known to contain hydrogen as a residual impurity (Clerjaud, 1991), it is inferred that OH-related centers are formed in GaAs. The stress splitting of this LVM does not fit the

6.

SOME ATOMIC CONFIGURATIONS OF OXYGEN

I

243

'

LINE 14 6K res. =0.06ciii-l

3285.0

3295.0 3305.0 WAVI:NlIMRER (cm-1)

FIG.29. Enlarged portion of the ahsorption of an OH LVM at 3300 c W ' (Line 14) in Sl GaAs showing the very weak '*OH \atellite ( B . Pajot and C. Song (1992a). Phys. R e v . B 45, 6484).

usual pattern for (100); ( 1 10) or ( 1 I [)-oriented dipoles. The fact that more components are observed than expected does not mean here a dipole with a low symmetry because of the full polarization of the components for simple orientations. This is interpreted as an OH radical weakly coupled to its environment, which can reorient under stress in directions different from the ones at zero stress (Pajot and Song, 1992a). This OH center is electrically active, and it can trap a hole, giving a new LVM at 3296 cm-' (Fig. 30). The small change in frequency suggest that the hole is not trapped by the 0 - H bond but by its environment. Among the other high-frequency LVMs, one at 2947 cm- has been related with certainty to N H in a trigonal site, but from their frequencies other LVMs must be related to other kinds of OH centers (Pqjot, Song and Porte, 1992b).

'

VII. Summary

Silicon, germanium and GaAs are three semiconductors for which relatively detailed information exists on interstitial oxygen, oxygen-vacancy centers and a few combinations of oxygen with impurities, dopants and lattice atoms. There is however a large variety of centers containing one or few 0 atoms for which no detailed microscopic information is available. This is especially true of the precursors of the thermal donors in silicon and germanium and of the complexes formed by migration of 0 or dissociation of simple 0-containing defects. The situation in GaP is not so clear and a LVM at 1020 cm- I has been tentatively attributed

244

B. PAJOT

b I

,

3293.0

,

,

,

1

3295.5

'

3298.0

'

'

'

I

"

3300.5

I ,

3303.0

WAVENUMBER (cm-1)

FIG.30. Absorption of OH LVMs near 3300 cm-' in SI GaAs: (a) under thermal equilibrium; (b) after 10 min. illumination with white light. Line 13 corresponds to the complex giving line 14 after trapping of a hole. The lines were labeled by integers in order of increasing energy ( B . Pajot and C. Song (1992a). Phys. Rev.B 45,6484).

(Barker, Berman and Verleur, 1973) to v3(Oi).In GaP again, the electrical and optical properties of 0 as a deep center have been discussed at length (Dean, 1986). The 0 atom related to this deep center is presumably substitutional. In II-VI compounds, because of the larger ionicity of the matrix, it seems possible for 0 to locate on an anion site, where it can behave as a deep isoelectronic trap in ZnTe (Merz, 1968), but it has been recently reported from PL data that it could also act as an acceptor in other II-VI compounds due to a charge transfer from the host lattice (Akimoto et al., 1992). Oxygen has been detected in diamond by fusion analysis and by CPA, and it is possible that a very small portion of this oxygen is present in the dispersed form (Walker, 1979). In that case, substitutional location seems more likely than interstitial. ACKNOWLEDGMENTS Some of the results described in this chapter were obtained in close collaboration with C. Song, and I wish t o acknowledge her competence and tireless activity. I am indebted to R. C. Newman for discussions and the communication of unpublished results. Discussions with C. A. J. Ammerlaan and R. Jones are also gratefully acknowledged. Special thanks are due to K. Lassmann for discussions on phonon spectroscopy and the communication of unpublished results. I take this opportunity to thank all the coauthors of our papers quoted in this chapter. Isotopically enriched samples were kindly provided by C. A. J.

6.

SOME A I O h l l ( (ONFIGUK4TIONS OF OX LGE N

245

Ammerlaan and J. M . Spaeth. I am a l s o indebted to P. Clauws and S. McQuaid tor discussions and for providing samples. Cutting w n p l e s for stress measurements was competently performed by C. Porte. 1 was greatly helped in computer-assisted drawing of defect models by V . Fabart and Y Zheng. Thi? work was supported in part by DRET.

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Hjalinarson. H. P . . and Jennison. D. K. (19x5). Phvs. R e v . B 31, 120X. Hrostowski. H. J.. and Alder. B . J . (1960).1.C'hem. Phvs. 33, 980. Hrobtow\ki. H. J . , and Kaiber, R . H . (1957). Phy.7. Ret,. 107, 966. Jagannath. C.. and Ramdas. A. K. (1981). Phys. Rev. B 23, 4426. Jastrzebski. L..Zanmcchi. P., Thebault. I),, and Lagowski, J. (1982).J . Electrochem. Sor. 129. 1638. Johnson. N. M. 11985). P l i y s . R w . R 31. 5525. Johnson. N . M.. Herring. C . , and Chadi, I). J. (1986). Phvs. Re),. Lett. 56, 769. Johnson. N . M.. Doland, C . . Ponce. F.. Walker. J . , and Anderson. G. (1991). Physicu B 170, 3 . Jones, C. E.. Schafer-, D., Scott. W . and Huger. R. J. (1981). J. Appl. Phys. 52, 5148. Jones. R . . and Oberg, S . (1992a). Phys. Rei.. Lert. 68, 86. Jones. R . . and b e r g . S. (1992b). Pltvs. R e v . Leri 69, 136. Jones. R . . Umerski, A . , and Oberg. S. (1992). Phys. Rev. B 45, 11321. Kaiser. W. (1962). J . P h s s . Chrm. Solids 23, 2 5 2 . Kaiser. W.. and Keck. P. H. (1957). J . Appl. Phys. 28, 882. Kanamori. A , . and Kanamori, M. (1979). J . Appl. Phvs. 50, 8095. Kaplyanhkii, A. A. 11964). Opr. y Sp(~krr-okopyia16, 602 ( O p t . S p e c f p . 16, 329). Kaufmann. U . . Klausmann. E.. Schneider. J.. and All. H. C. (1991). Phys. Rev. B 43, 12106. Kellrr. W. W. (1984). J . Appl. Phy.5. 55. 3471. Khirunenko. L. I . . Shakovstov. V . I . . Shinkarenko. V . K., and Voroblako, F. M. (1990). Fiz. Tekh. P o l u p r o i m h . 24, I401 (Soi,. Phvs. Semicond. 24, 663). Kimerling, L. (1977). In Rudiafion bJfi,ct,s in Sr~mic.~~ndirc.rors. lY76, N . B. Urli and J . W. Corhett (eds.),p. 3-21, Institute o f Physics. London. Krishnan. K.. and Hill, S. L. (1981). I n Fourier 7runsform Infrared Specrroscopy H. Sakai led.). p. 27. S.P.I.E. 289. S.P.1 E.. Hellingham. Wash. Lappo. M . T.. and Tkachev. V . D. (1970). I??. Tehk. Poluproiwdn. 4, SO2 iSov. P h v s . .Srrnic.ond. 4. 418). Lee. Y. H.. and Corbett. J. W. (1976). Phv.t. Rev. B 13, 2653. Lin. A., (19x2). J. Appl. Phys. 53, 6989. Lindstrdm, J . L.. and Svensson. B. G . (1986). Mor. Kes. SOC.Symp. Proc. 59, 45. IAvinov. V . V.. Urenev, V . 1.. Shershel'. V . A. (1983). Fit. Tekh. Poluprovodn. 17, 1623 (S'OI.. Phy:,. Semicond. 17, 1033). Martin. G . M.. and Makram-Ebeid. S. (1986). In Deep Centers in Semicmducrors, S . T. Pantelides (ed.). p. 399. Gordon 6t Hreach. New York. Meese. J . M.. Farmer, J. W., and Lamp, 10 A) or a unqiue fast diffusion path for oxygen pairs exists.

282

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Research on TD properties and formation reactions is important because it addresses the early stages of aggregation of oxygen in silicon. The donor activity must be controlled to maintain doping uniformity as circuit integrated levels increase. Control of oxygen precipitation nucleation and growth is key to processing defect-free devices and contamination gettering. TD research has, also, added fundamental insights into the understanding of shallow level impurities in semiconductors. TDs have provided both a source of new knowledge and a basis for process technology design. 111. New Donors

Donor states due to heat treatment of Cz silicon material at temperatures between 650°C and 800°C have first been reported by Liaw and Varker (1977) and Grinshtein et al. (1978). Kanamori and Kanamori ( 1979) demonstrated that TDs and the high-temperature donors, called N e w Donors (ND) show significantly different annealing behavior. TDs annihilate at 550°C while NDs are generated at temperatures above 550°C. The ND generation depends on the preannealing conditions. Only at 470°C to 550°C do preannealed samples produce ND in Cz silicon. It was found that a high carbon concentration ([C] > 2 x 10l6~ m - also ~ ) promotes the formation of NDs without a low-temperature preanneal. Annealing experiments with oxygen-diffused FZ silicon also produced NDs. This demonstrated that oxygen is essential for the ND formation. Figure 20 shows the donor generation in dependence of the annealing temperature. There are two temperature regimes in which donors are formed: at 450°C TDs are generated and around 750°C NDs appear. NDs can be partially annihilated at temperatures above 1000°C. A heat treatment of 10 hrs at 1000°C reduces the ND concentration by 50 to 80% (Cazcarra and Zunino, 1980). Cazcarra and Zunino (1980) also studied the formation kinetics of the NDs. They found that the formation kinetics of the NDs are closely related to the formation of oxygen precipitates. Therefore they suggested that NDs are related to Si,O,r clusters of a few hundred atoms of oxygen acting as nucleation centers for oxygen precipitation. Carbon was suspected to play a major role in the formation of new donors. Leroueille (1981) showed that with the formation of NDs the IR absorption band of carbon at 16.5 pm decreased indicating that carbon is involved in the formation of NDs. Gaworzewski and Schmalz (1983) suggested that carbon is involved in the nucleation process of NDs through formation of ( C , 0) complexes. They demonstrated the importance of carbon as a site of nucleation for ND formation and oxygen

7.

ELECTRICAL P K O t ' t R T IES OF OXYGEN IN SILICON

I

' A '

11

I

I

I

283

I

initial O x y g e n (pprna) 0 40

A 37 24

1

700

900

0 32 I

300

500

Anne;iling Tcmperature (OC) Ficj. 20. Maximum donor generation pel- h o w ( M . D . G . H . )of annealing at a given temperattire i n a nitrogen ambience. (C'arcarr;~and Zunino, 19x0).

precipitation. These (C, 0) complexes of different size were tentatively identified as NDs. A study of the formation of NUS by Kamiura, Hashimoto, and Yoneta (1991) shed new light on the nucleation of NDs. DLTS spectroscopy revealed three different traps connected with NDs. It was shown that different kind of NDs were formed depending on the carbon content and preannealing conditions. One DLTS band was correlated with the presence of carbon in the sample while another band existed only in connection with rodlike defects after a preannealing at 450°C. The third DLTS band was found in preannealed samples with high carbon content. These results show that depending o n the material and the annealing conditions different NDs are observed. They could also explain the different models that are proposed for NDs.

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There are two models that explain the origin of the electronic states of NDs. Holzlein, Pensl, and Schulz (1984) developed a model based on the similarity of the DLTS spectra of NDs and Si-SiO, interfaces. This model proposes a continuous distribution of ND deep levels originating from states at the surface of SiO, precipitates. The donorlike behavior was explained by a fixed positive charge associated with the precipitate. Such a fixed positive charge was found in the oxide near the Si-SiO, interface of planar MOS structures. In a further study on hydrogenation effects on NDs, Holzlein et al. (1986) came to the conclusion that interface states at the surface of the SO, precipitates as well as bound states in the Coulombic well of a fixed positive charge contribute to NDs. A second model to explain the electrical activity was put forward by Babich et al. (1988). Based on EPR and Hall-effect measurement it was proposed that NDs are due to extensive fluctuations of the crystal potential on which electrons can localize. These fluctuations are caused by the formation of oxygen clusters that lead to a crystal lattice distortion near their boundaries. With these assumptions it was possible to explain the linear shift of the g-factor as well as asymmetry, anisotropy, and EPR line width and their dependence on the annealing conditions. From the DLTS experiments it becomes evident that NDs are a collection of several different defects. Oxygen is involved in these defects. There is little disagreement that NDs are due to extended defects, whether as oxygen clusters or as oxygen precipitates, but there is no agreement on the structure of the donor. Until now structure sensitive experiments like ENDOR have not been applied to NDs successfully.

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Stavola, S. J. Pearton, and G. Davies (eds.), MRS Symposia Proceedings Vol. 104, p. 185. Materials Research Society, Pittsburgh. Michel, J., Niklas, J. R., and Spaeth, J. M. (1989). Phys. Rev. B 40, 1732. Michel. J.. Niklas, J . R., Spaeth, J. M., and Weinert, C. M. (1986). Phys. Rev. Lett. 57, 611. Muller, S. H., Sprenger, S . , Sievers, E. G., and Ammerlaan, C. A. J. (1978). Solid State Comm. 25, 987. Murray. R., Brown, A . R..and Newman, R. C. (1989). M a t . Sci. Engineering B4, 299. Needels, M.. Joannopoulos, J . D., Bar-Yam, Y., and Pantelides, S. T . (1991).Phys. Rev. B 43, 4208. Newman. R. C. (1985). 1.Phys. C 18, L967. Newman. R. C., Brown, A . R.. Murray, R., Tipping, A,, and Tucker, J . H. (1990). In Pruc. 6rh I n f . Symp. Silicon Muter. Sci. Technol.-Semiconducfor Sci. H. R. Huff, K. G . Barraclough, and J. Chickawa (eds.), Electrochem. SOC.Proc. Vol. 90-7,p. 743. Oder, R.. and Wagner, P. (1983). In Defects in Semiconductors 11, S. Mahajan and J . W. Corbett (eds.), MRS Symposia Proceedings Vol. 14,p. 171. North-Holland, New York. Oehrlein. G . S . , Lindstrom, J . L., and Cohen, S. A. (1984). In Proc. o f t h e 13th I n t . Cmf. ow Defiers in Semiconductors. L. C. Kimerling and J. M. Parsey, Jr. (eds.). p. 701. The Metallurgical Society of AIME, Warrendale, Pa. Ourmazd A.. Schroder, W., and Bourret, A. (1984). J. App1. Phys. 56, 1670. Pajot, B., Compain, H . , Lerouille, J . , and Clejaud, B. (1983). Physica 117B-l18B, 110. Pajot, B., and von Bardeleben, J. (1984). In Proc. of the 13th I n t . Conf. o n Defecfs in Sen7iconductors, L . C. Kimerling and J . M. Parsey, Jr. (eds.), p. 685. The Metallurgical Society of AIME, Warrendale, Pa. Pearton. S. J . . Chantre, A., Kimerling, L. C., Cummings, K. D., and Dautremont-Smith. W. C. (1986). Proc. Muter. Res. Soc. 59, 475. Robertson. J.. and Ourmazd, A. (1985). Appl. Phys. Lett. 46, 559. Snyder, L. C., DeBk, P., Wu, R. Z., and Corbett, J. W. (1989). In Proc. of the / 5 t h Int. Conf. on Defects in Semiconductors. G . Ferenczi (ed.), Materials Science Forum Vols. 38-41, p. 329. Trans Tech Publications, Zurich, Switzerland. Stavola, M . and Lee, K . M., (1986). In Oxygen, Carbon, Hydrogen and Nitrogen in Silicon. J . C. Mikkelsen, Jr., S. J . Pearton, J. W. Corbett, and S. J . Pennycook (eds.), MRS Symposia Proceedings Vol. 59, p. 95. Materials Research Society, Pittsburgh. Stavola. M., Lee, K. M., Nabity. J. C.. Freeland, P. E., and Kimerling. L . C. (1985). Phys. Rev. Lett. 54, 2639. Stavola. M.. Patel, J . R., Kimmerling, L . C., and Freeland, P. E. (1983). Appl. Phys. Leu. 42, 7 3 . Stavola, M..and Snyder, L. C. (1983). In Defects in Silicon. L. C. Kimerling and M. Bullis (eds.). p. 61. The Electrochemical Society, Pennington, N.J. Steele. A . G . , and Thewalt, M. L. W. (1989). Can. J. Phys. 67, 268. Suezawa, M.,and Sumino, K. (1984). Phys. Srat. Sol. ( a ) 85, 469. Tajima. M., Kanamori, A , , and lizuka, T. (1979). Jpn. J. Appl. Phys. 18, 1401. Thewalt. M . L. W., Steele, A . G . , Watkins, S . P., and Lightowlers, E. C. (1986). Phvs. R e v . Left. 57, 1939. Tkachev, V. D., Makarenko, L. F.. Markevich. V . P., and Murin, L . I . (1984). Sov. Phys. Seinic.ond. 18, 324. Wagner. P. (1986). In Oxygen. Carbon. Hydrogen and Nifrogen in Silicon,J . C. Mikkelsen, Jr., S . J . Pearton, J. W. Corbett, and S. J. Pennycook (eds.). MRS Symposia Proceedings Vol. 59, p. 125. Materials Research Society, Pittsburgh.

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ELECTRICAL f’KOPtRTIES O F OXYGEN IN SILICON

287

Wagner. P.. Gottschalk. H . . Tromhetta. I . . and Watkins. G . D. (19x7). J . Appl. PAY\. 61, 346. Wagner. P.. and Hage. J . (1989). A p p l . P/I?J.A 49, 123. Wagner. P.. Holm, C.. Sirtl. E.. Oeder. K . , and Zulehner. W. ( 19x4). In A d i ~ t i ~ it7 r sS o l i d Sicita Phvsic~s.P. Grosse (ed.). V o l . 24, p. 191. Vieweg-Pergamon, Braunschweig. i Nilrogczn in Weber. J.. and Queisrer. H . J . (1986). In O.rygun. Curbon. H y d r ~ g ~ rcind Silicon. J . C . Mikkelsen. Jr . S . J . Pearton. J . W. Corbett. and S. J . Pennycook leds.1. MRS Symposia Proceedings Vol 59. p. 147. Materials Research Society. Pittsburgh. van Werep. 0 . A , . Gregorkiewici. -1- . Lkkman. H . H . P. T.. and Ammerlaan. C. A . J . 1986). In Dqfc>cis in Srtnicondirt IIJU. H . J . von Bardeleben (ed.). Materials Science Forum Vols. 10-12, p. 1009. Tian\ Tech Publication Ltd.. Switzerland. Wruck. 0 . . and GaworLewski. P. (1979).P h \ > s . Stcii. Sol. ( t i ) 56. 557. Wruck. D.. and Spiegelberg. F. (1986). Pliv\. S i ( i r . S o l . ( b ) 133. K39.

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S t M l C O N D U ( IOHS A N D SEMIMETALS. VOL 42

CHAPTER 8

Diffusion of Oxygen in Silicon R . C. Newman INTERDISCIPLINARY RESEARCH

< FNTRE

FOR SEMICONDUCTOR MATERIALS

THE BLACKETT LABORATORY IMPERIAL COLLEGE O F SCIFNC I

, TE< HNOI OGY

AND MEDICINE

I O N D O N , UNITED KINGDOM

und R . Jones DEPARTMENT O F PHYSICS UNIVERSITY O F EXETER, l J N l l E D KINGDOM

1. 11.

INTRODUCTION . . . . , . . . . . . . . . . . . . . DIRECTMEASUREMENTY OF NORMAL OXYGEN DIFFUSION . . . I . Single D$fusion J u m p s . . . . . . . . . . . . . . 2 . Profiles . . . . . . . . . . . . . . . . . . . . 3. Summary . . . . . . . . . . . . . . . . . . .

111.

INDIRECTMEASUREMENTS OF NORMAL OXYGEN DIFFUSION. . I . D,,,, Determined ,from Oxygen Precipitation ut High Temperutures . . . . . . . . . . . . . . . . . . lit Intermediate Temperatures . . 3. Oxygen Aggregtrtion N I L O N ,Temperurures . . . . . . ENHANCED OXYGEN DIFFUSION NOT INVOLVING HYDROGEN. I . Effects Due to the Injrc.tion of Vacancies und I-Atoms h! 2 MeV Electron lrrudiution . . . . . . . . . . . 2 . The Effect of E.rt ('.\A I-Atoms . . . . . . . . . . . 3. Rtipid Diffusion of' Di-O.rygen De.fec,ts . . . . . . . . 4. Effects Due t o Curhon . . . . . . . . . . . . . . 5 . Fffects Due t o Mrtirllic. Conrumination . . . . . . . 6. S u m m u y . . . . . . . . . . . . . . . . . . . . SILICON CONTAINING HYDKOC~EN IMPURITIES . , . . . , . I . Silicon Heated in Hydrogen Gus . . . . . . . . , . 2 . Silicon Heated in uti RF Pltrstnu . . . . . . . . . . 3. A n Outline Model tincl S u m i n u p . . . . . . . . . . THEORETICAL MODEII N G ot OXYGEN DIFFUSION. . . . . . I . The.orrtica1 Methods . , . . . . . . . . . . . . . 2. Theory o f the D(ffii.rion Constunt . . . . . . . . . . 3. Intrrstitiul Oxvgen . . . . . . . . . . . . . . . . 4. Diflusion of 0, ('trtu1y:ed by Hydrogen . . . . . . . S. The 0.rygen Ditticr . . . . . . . . . . . . . . . 6. Other 0.rygen Aggregtrtes , . . . . . . . . . . . .

2 . C).rygen Aggregution

IV.

V.

VI.

V11. CONSTRAINTS ON MODFI.SOF THERMAL DONORCENTERS . . .

290 292 293 296 298 298

299 303

305 308 309 312 314 316 317

317 718 31Y

323 324 326

327 33 I 332 335 339 34 I 342

289 Copyright IE, 1994 hy Academic he\,. Inc All nght5 of reproduction in any form re\erved ISBN 0-1?-7S?14?-Y

290

R. C. NEWMAN A N D R. JONES

VIIl. SUMMARY . . . . . . . . . . . . . . . . . . . . . Acknowledgmenls . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . .

345 347 347

I. Introduction

Silicon grown by the Czochralski pulling technique contains oxygen impurities in a concentration close to 10" ~ 1 1 1Early ~ ~ . X-ray diffraction measurements showed that the lattice parameter, a,, was increased when oxygen was present, demonstrating that the atoms occupy interstitial sites (Bond and Kaiser, 1960). High-resolution infrared (IR) absorption measurements of the now well-known 9 km band and other associated bands due to the vibrations of the oxygen impurities then led to the conclusion that the atoms were located in off-axis bond centered positions, written as 0, (Chapter 5). The bonding to two silicon neighbors explains why there is no electrical activity of such atoms. However, diffusion of Oiatoms during annealing around 450°C leads to the formation of small clusters that act as double thermal donors (TD) (Chapter 6), while the precipitation of particles of SiOz at much higher temperatures (Chapters 9 and 12) is also a consequence of 0; diffusion. There was a clear need to determine the diffusion coefficient Doxyover a wide range of temperature (Section 11) but this has been no easy task. Electrical methods used for the determination of high-temperature indiffused profiles of group I l l and V elements (Fuller and Ditzenberger, 1956) are not applicable, and neither is there a suitable radio tracer, comparable with I4C used for diffusion measurements of electrically inactive carbon (Newman and Wakefield, 1961, 1962). Early measurements of Doxy,although well-conceived, ingenious and pioneering, particularly those obtained from measurements of internal friction (Southgate, 1957, 1960; Haas, 1960) and the relaxation of stress-induced dichroism of the 9 k m IR band (Corbett and Watkins, 1961; Corbett, McDonald and Watkins, 1964a), were therefore limited in number. It is only relatively recently that additional reliable values, determined from profiles measured by secondary ion mass spectrography (SIMS) have become available for T 2 650°C (Mikkelsen, 1982a, 1982b; Lee and Nichols, 1985; 19861, although other SIMS measurements in carbon-doped silicon have shown anomalies (Shimura, Higuchi and Hockett, 1988). It was then shown that the rate of precipitation of SiO, in the same temperature range was diffusion limited with the same value of Doxy(Section 111). In a middle range (400°C to 700°C) there are no microscopic measurements, while SIMS measurements have again shown anomalies (Lee and Fellinger, 1986; Fellinger and Chen, 1988; Gosele et al., 1989) (Section IV). At lower

8. DIFFIISION

O k O X Y G E N IN SILICON

29 1

temperatures (270°C to 400"c'), further determinations of Don) have been made from the rate of relaxation of stress-induced dichroism of the IR 9 pm absorption band (Stavola et al., 1983; Newman, Tucker and Livingston. 1983b). The values so obtained agreed with the extrapolation of the high-temperature internal friction and SlMS data, but only for certain samples. Stress-dichoism measurements made on samples given a postgrowth heat treatment have shown enhanced values of Doxy(Stavola et al., 1983). appearing to support other claims of much greater enhancements based on indirect evidence (Berghok, Hutchison and Pirouz, 1985: Gaworzewski and Ritter, 1981). These claims have given rise to attendant speculation, extending over some 35 years (Section IV). It is not sufficient to invoke enhanced diffusion to explain particular observations: the circumstances leading to the enhancement must be fully identified. followed by the proposal of a microscopic model. This model should be checked by ancillary experiments (Section V ) , and its plausibility should also be examined by theory (Section V1). Much progress has been made but we do not yet have definitive answers to certain k e y questions that have been raised. Much of the confusion ha3 arisen because interactions of 0,atoms with both lattice vacancies (Bemski. 1959; Watkins and Corbett, 1961; Corbett et al., 1961) and self-interstitials (I-atoms) (Brelot and Charlemagne, 19711 have been clearly demonstrated (Section IV), I-atoms are known to be generated during precipitation of oxygen for T > 500°C (Bourret. 1986),and there is long-standing but rarely quoted indirect evidence that 0; atoms interact with fast-diffusing hydrogen atoms (Fuller and Logan. 1957) (Section V ) . In addition, theory has indicated that oxygen pairs (O,)?,formed in the early stages of oxygen aggregation. have a diffusion coefficient greater than that of isolated 0; atoms (Sections 1V and V I ) (see also Gosele and Tan, 1982). centers have not been detected spectroscopically (Kinierling, 1986) although the formation of O2C, complexes, where C, i s an interstitial carbon atom (Kurner et al., 1989). provides some plausible indirect evidence for their existence. Interactions between 0, atom5 and C, atoms have also been invoked to explain enhanced 0,diffusion at high temperatures (Shimura et a\., 1988). It is important to point out that related first principles theory is gaining in importance as the strengthh and weaknesses of various procedures are evaluated. There is no doubt that the procedures have improved over the years. while the available computing capacity has increased to make calculations more realistic and hence more reliable. As this has happened, there has been a shift in the predictions relating to oxygen diffusion processes. This work is not yet definitive. and in that sense, it mirrors the experiments. A full discussion is given in Section V1.

292

R. C . NEWMAN AND R . JONES

0

SILICON ATOM OXYGENATOM

FIG.1 . Geometry of a bonded interstitial oxygen impurity in silicon showing the off-axis site, the mean diffusion jump distance d and the bond populations nl-n4.

After reviewing these various topics, we can state the most likely scenarios as they appear at present and give the consequences when there is more than one option (Section VII). In particular, the number of oxygen atoms that can aggregate to form a thermal donor in a given time will depend not only on D o x y but , on whether or not (Oi)* pairs diffuse more or less rapidly than single Oiatoms. Our overall conclusions are set out in Section VIII. 11. Direct Measurements of Normal Oxygen Diffusion

Oxygen diffusion jumps are presumed to be from one bond-centered site, a mean position when allowance is made for the rotational motion, to an equivalent adjacent site (Fig. I). The jump distance d is equal to (2/3)% = (2)”*u0/4 = 1.92 A, where a is the Si-Si nearest neighbor separation. Doxyis equal to d 2 / T , where the reorientation lifetime T (for a diffusion jump) is given by T~ exp (E,/kT) at a temperature T . Thus Doxy = Do exp ( - E,/kT), with Do = 2a2/37 = 4 / 8 7 , if the diffusion jumps are uncorrelated. The lowest measured values of Doxyat a given Tare taken

8.

293

DIFFLI\ION O F OXYGEN IN SILICON

to define normal diffusion. There is no evidence that intrinsic defects or other impurities are involved or that the rate is dependent on the position of the Fermi level F~ (Lee and Nichols, 1985: Hahn, 1986). Larger values of Dox,have been reported (Sections IV and V) and must be equal to the (normal) and D,,,, (enhanced), involving processes in which sum of Doxy defects or a second impurity interact with the 0, atom.

I . SINGLE, DIFFUSION JUMPS The fact that the local symmetry of an 0, atom is not tetrahedral has been used to great advantagc. In a strain-free crystal the four bondcentered sites along ( 1 1 1 ) directions are equivalent. and the four associated populations r i l - i i j of 0,atom3 are equal. However, if a uniaxial stress is applied along a [ I 1 I1 direclion, atoms with this bond axis experience an interaction energy three times greater than that of atoms in the other three ( I 1 I ) axes (a factor of cos (70.5')). The population ti, will decrease, ;is a result of diffusion jumps to the neighboring bonds, and n, = n , = t i j will increase, provided the temperature is high enough for the jumps to occur. The application of acoustic waves with a stress component parallel to ( I I I ) leads to an alternating jumping process that produces damping of the mechanical vibrations. The position of the damping peak 8 the occurs when COT* = 1, where w is the angular frequency, T* = ~ / is time constant measured experimentally and the shape of the curve provides further information about the resonance (Southgate, 1960; Haas, 19h0). From the geometry of the bonds (Fig. 1 j we deduce

dtlI/df =

(1/7)1 -

6t11 + 2r2,

+ 2n-3 + 2n41,

(1)

and three other equations with cyclic permutations of n,-tz,. The internal friction is proportional to ?' =

I?! - ( 1 / 3 ) ( t 1 ,

+ n , t n,)

= (Ill

-

n2),

(2)

for the stress parallel to ( I I I ) . We find dyldt = - @ / T = - Y / T * , so that Doxy = ~1'/127*or ~ $ 6 4 ~ ' Such . effects were measured as a function of temperature by Southgate (1957. 19601, who used either a 100 kHz or a 300 kHz source. These measurements also demonstrated that the axis of an 0, impurity was parallel to a Si-Si bond since no internal friction was found when the applied stress was parallel to a (001) axis. Haas analyzed Southgate's data to find the value of D,, and obtained Doxy= 0.21 exp ( -2.55eVlkT) em's-' for the range 1325°C > T > 850°C (Fig. 2 ) . These ideas were expanded and adapted to allow Doxyto be measured at much lower temperatures (33OT-40o"Cj from stress-induced dichroism in the oxygen 9 pm vibrational absorption band (Corbett and Wat-

294

R . C . NEWMAN A N D R . JONES

10.8

1000 800

Temperature "C 600 500 400

300

Doxy = 0.13exp(-2.53eV/kT)cm2s

0.6

0.8

1.0

1.2

1.4

1.6

1.8

1O O O / l (K-l)

FIG. 2. An Arrhenius plot of the oxygen diffusion coefficient, combining the internal friction data of Southgate (1957, 1960) and Haas (1960) (the solid line) (REFS h and i), the low-temperature stress dichroism data of Corbett et al. (1964a), Stavola et al. (1983). and Newman et al. (1983b) (REFS g, d and e), the high-temperature SlMS data for in-diffused profiles of Mikkelsen (1982a) and Lee and Nichols (1985, 1986) (REFS c and b), the X-ray data of Takano and Maki (1973) (REF f ) , together with the analyses of Gass et al. (1980) (REF a). The line Doxy= 0.13 exp ( - 2.53 eV/kT) cm2 s - ' is taken to define normal oxygen diffusion.

kins, 1961; Corbett et al., 1964a). Isotropic absorption occurs only if the 400°C for four populations ~ 1 - 1 1 4 are equal. Heating a sample to T 15-30 min while a uniaxial stress of 100 MPa is applied along a (1 1 1) axis leads to a decrease in n , and increases in n2 = n3 = n4 as explained earlier. This distribution is frozen in, on cooling the sample to room temperature with the stress still applied, at which stage the stress is removed. The absorption coefficients a , ,and aL for polarized light with the E-vector parallel and perpendicular to the stress axis respectively are proportional to ( n , 4 3 ) and (4n2/3),assuming that the dipole moment M I is , parallel to a bond axis. Expressions for a l / a I I(Table I) were given by Corbett et al. (1964a) for three stress axes, different viewing axes and

-

+

-

8. DIFFLI\ION

295

OF OXYGEN IN SILICON

IABLk I

1 H E DICHROIC RATIOa,/ulMFASLIRFO A 1 ROOMTEMPERATLIRE. FOR VARIOUS A N D ViFwih(I Axr5' (Corbett et al , 1964a) Stress Axis

Viewing Axis

< I 10>

rheory

MI. I I I

I y? 2 f

SlRrSS A X E S

0 1 /all

M

Expth

Predicted'

2 ( I + y?) 3y? + I

1.18

1.16

"'4stresh of 2700 kg c m - ' was applied for 30 min at 400°C. ? 0.07. '.4ssuming M < I I I >. 'Similar values were found for unstressed control samples. 'Used to predict the other value\

for M either parallel or perpendicular to ( 1 1 I ) . where p' = n z / n i and y' = t i 4 / ) i 3 . A discussion of the magnitude of the dichroism was also presented and shown to be consistent with that expected from Boltzmann statistics. On annealing, the normalized dichroism 3(a, - aI,)/(all+ 2a,) ( a , all)/a, of the 9 pm band decays exponentially with a time constant T * during a subsequent isothermal anneal, leading to the values of D,,, shown in Fig. 2 (Corbett et a l . , 196421; Stavola et al., 1983; Newman et al., 1983b). Alternatively. the induced dichroism and its loss can be measured for the weaker oxygen 19.5 pm band (517 c m - l ) . The frequency of this band falls in the continuum of lattice modes (Raman frequency 520 cm 1 and shows no isotopic shift when I6O is replaced by "0 and so, unlike the 9 pm band. it cannot be a true localized vibrational mode ( L V M ) (Newman, 1973). The absorption occurs because there is a dipole moment of the oxygen complex perpendicular to the Si-Si bond axis (Jones, Oberg and Umerski. 1992) and for a ( 1 1 I ) stress we have al,> a _ (Table I ) . The normalized dichroism i s smaller than that for the 9 pm band by a factor of two but the calculated relaxation time T * is the same. These conclusions were verified hy Stavola (l984), who demonstrated that the 19.5 pm (517 c m - ' ) band was indeed due to the presence of 0, atoms. rather than grown-in substitutional oxygen atoms, as proposed by

-

~

'

296

R. C. N E W M A N A N D R. JONES

TABLE 11

SUMMARY OF DATA FOR NORMAL OXYGEN DIFFUSION

’

D,(cm2s )

ED (eV)

Reference

0. I4 0. I3 0.23 0.21

2.53 2.53 2.56 2.55

Lee and Nichols, 1985 Mikkelsen, 1986 Watkins, Corbett and McDonald, 1982 Southgate, 1960; Hass, 1960

O’Mara (1983). The latter suggestion arose from the known sequence (Newman, 1973) of LVM frequencies for 1°B (644 cm-I), “B (621 cm-I), I2C (605 cm-I), 13C (586 cm-I), I4C (570 cm-I), and I6O (530 cm-’-540 cm-’) (extrapolated). In practice, it is better to make dichroism measurements of the 9 pm band because a superior signahoise ratio can be achieved. However, the 19.5 p,m band can be used, as in the work of Freeland (1980) and Newman et al. (1983a, 1986b), and there would be an advantage if there were absorption from precipitated S O , underlying the 9 p.m band. In summary, the results of the dichroism measurements are in complete agreement with those obtained from the internal friction measurements (Fig. 2; Table 11). 2. PROFILES Diffusion of oxygen into or out of as-grown material containing Oi atoms in a concentration c,, has been studied under conditions where the surface concentration has a constant value of c, corresponding to the solubility and resulting from a coating of SO,. Assuming that there is no surface rate limitation and that internal precipitation does not occur to any significant extent, the diffused distribution is given by c(x, t ) = c, e r f c [ x / ( 2 ~ t ) ~+’ ~~,erf[x/(2Dt)”~)]. ]

-

(3)

In float-zone silicon the value of co is usually less than 10l6 atom cm-3 and there will be a net in-diffusion at all temperatures for which the solubility c , exceeds co. On the other hand, if cois large, as in Czochralski silicon, there will usually be a net out-diffusion. To find values of Doxyit is necessary to determine the distribution c ( x , t ) . Logan and Peters (1957, 1959) had the ingenious idea of making hightemperature in-diffused oxygen profiles electrically active by giving such samples a second heat treatment at 450°C to produce small oxygen aggregates that acted as donors (thermal donors). The original oxygen distribu-

8.

DIFFII5ION O F OXYGEN IN SILICON

297

tion could then be quantified from subsequent measurements of the conductivity as a function of depth from the surface. In their second paper, they took account of the observations of Kaiser, Frisch and Reiss (1958) that the initial rate of donor formation and the maximum concentration that was attained varied as the fourth and third powers of the oxygen concentration, respectively. Similar measurements were carried out later by Hu (19811, Gaworzewski and Ritter (1981), and Isoma, Aoki and Watanabe ( 1984). Data obtained for high-temperature diffusions were in reasonable agreement with those obtained by internal friction, but it is now known that there could have been complications. The concentrations of the various types of donor (TDI, TD2, TD3, etc.) that are formed sequentially have different dependences on c , , (Wagner, 1986), while negligible rates of TD formation near a surface have been reported by Hahn (1986). Another early analysis was carried out by Takano and Maki (1973). who obtained depth profiles of the lattice parameter u,, from X-ray measurements after the successive removal of layers of material. Oxygen concentrations down to I O l 7 cm ~'could be detected in samples diffused in the range 1 100°C-1200"C, and values of Doxywere in excellent agreement with those obtained by internal friction and SIMS (Fig. ?). Indiffused oxygen has also been quantified by charged particle analysis (Gass et al., 1980; l t o h and Nozaki, 1985). Further discussion of these topics has been presented by Mikkelsen (1986). By far the most important measurements, covering a wide range of 7 (700"C-l40O"C) are those obtained by the SIMS technique, first for in-diffused profiles (Mikkelsen, I982a. 1982b) and then for out-diffused and further in-diffused profiles (Lee and Nichols. 1985. 1986). Mikkelsen used enriched "0 as a diffusant to improve the SIMS sensitivity, which is otherwise limited by residual "(1 contamination in the vacuum system. to give a background --loi7 c m - ': use of "0 reduced this level by a factor of -100. Measurements were possible only for 7 2 700°C because at lower temperatures the depth of the protile was limited by the low values of D,,,, and the surface concentration c , (see Section 111). The combined data are shown in Fig. 2 . Other out-diffusion measurements made by SIMS following annealing made at II0O"C (Heck, Tressler and Monkowski, 1983) were interpreted in terms of small enhancements or retardations of D o x ydepending . on the heating ambients. The small overall spread in the values of Doxyof 7.8 z 0.3 x lo-" em's-', where = 7.8 x l o - " ern's-' is the value quoted by Mikkelsen (1986). cannot in our opinion be considered to be sufficiently large to justify the claim nor the proposal that the diffusion occurs by a vacancy process. The source of the oxygen used by Mikkelsen was enriched water vapor

298

R . C. NEWMAN AND R . JONES

H2’*0so that there would have been simultaneous in-diffusion of hydrogen (McQuaid et al., 1991; Veloarisoa et al., 1991). There were no obvious effects on the oxygen diffusion rate arising from the presence of the hydrogen, although enhancements occur at temperatures T < 500°C (see Section V). Hydrogen-oxygen interactions in plasmas are also important as implied by Hansen, Pearton and Haller (1984), but the introduction of lEO into a plasma did not lead to in-diffused concentrations of oxygen that could be detected by SIMS (Mikkelsen, 1986).

3 . SUMMARY To conclude this section on “normal” oxygen diffusion, parameters for Doxygiven by various authors, including combinations of the low- and high-temperature data (see Watkins et al., 1982), are given in Table 11. The linkage of the high- and low-temperature microscopic measurements provides convincing evidence for the model of Oi jumps from one bond center to the next, without the involvement of an intrinsic defect or a second impurity, including a second Oi atom. The diffusion jumps occur, with an activation energy close to 2.5 eV, over the whole temperature range from the melting point of silicon down to 250°C. However, longrange diffusion is known to have this activation energy only for T 2 700°C. In the later sections we shall evaluate Doxyfrom the expression Doxy= 0.13 exp (-2.53 eV/kT) cm-? s-l given by Mikkelsen (1986). It is interesting to find that this expression does not differ in any significant way from that deduced from the work of Southgate and Haas in 1960 (Table 11). Measurements that have implied enhanced diffusion were made at temperatures T 5 650°C except for the results presented by Shimura et al. (1988) and Shimura (1991). For the proposals that are vindicated, it would be reasonable to infer mechanisms that have activation energies less than 2.5 eV.

111. Indirect Measurements of Normal Oxygen Diffusion

In Section II.2., the out-diffused oxygen profile to an external planar silicon surface was discussed. Measurements of c(x, t ) by SIMS led to values of Doxy,with the assumption that there was no rate limiting process at the surface. Alternatively, IR measurements of the 9 pm band could have been made and fitted to the expression [c, - JE c(x, t ) d x ] , to give the loss of Oifrom solution as a function of time, since the reduction in the integrated absorption coefficient of the 9 pm band can be converted to AIOj] using the calibration data of Baghdad; et al. (1989). Corresponding

8.

D I F F U S I O N OF O X Y G E N I N SILICON

299

measurements of A[O,] resulting from the growth of internal precipitates of SiO, will also lead to values of D,,,,. if the size and number density of the particles are known, and if it is assumed that there is no rate limiting interfacial process. Direct measurements of the rate of growth of SiOz particles can be made by TEM or SANS without ambiguity for Czochralski silicon heated to temperatures T 2 650°C. Some duplication of the information presented in Chapters 4 . 9 and 10, is necessary to show that values of D,,,, deduced from high-temperature precipitation kinetics agree with those for normal diffusion, so that extrapolations to lower temperatures might be justified. We shall discuss three temperature ranges: (a) high temperatures ( Z 2 SSOOC), where SiOz particles form, (b) intermediate temperatures 500°C 5 T 5 650"C, where ribbonlike contrast is found in transmission electron micrographs. and (c) low temperatures ( T 5 SOO"c'), where thermal donors are produced. The aim is to relate measurements of the rate of loss of oxygen from solution. A[O, ]/At. to models. to obtain a coherent and self-consistent overview for the whole range of temperature. For T < 650°C the known facts are limited and the validity of proposed interpretations remains subjective. 1. D,,xy DETERMINED FROM

O X Y G E N PREClPlTATlON AT HIGH

TEMPERATURES

The rate of growth of SiOz precipitate particles during the early strrges of high-temperature annealing ( 7 ' z 650°C) is easily quantified if 0, diffusion is the rate limiting process. The number of 0, atoms per unit time that cross a spherical surface surrounding a diffusion sink with a capture radius rr is then given by 47rc,)1',1). I f I', ( 1 ) is set equal to the radius r,, of a "large" growing (spherical) precipitate, we obtain 1'5 = (2c,)D/c,,11, where c'p = 4.6 x 10" cm- is the concentration of oxygen atoms in SiO,. The grown-in oxygen concentration co can be determined by IK spectroscopy, while the size of the particles, which have been shown to be nearly spherical in the early stages (Gupta et al., 1990), can be measured by TEM or SANS. The two methods give equivalent results. relating to real space and reciprocal space, respectively (Bergholz et al., 19891. but the latter is preferred as i t leads to an average value for the whole volume of the sample. Measurements made on a sample heated at 750°C (Fig. 3 ) led to a value of D equal to the normal value of Doxy (Fig. 4). within the experimental errors (Livingston et al.. 1984). Thus, it was demonstrated that long-range 0, diffusion controls the rate of precipitate growth at this temperature, rather than a surface reaction such as the formation and outward diffusion of self-interstitials (/-atoms) required to accommodate the local increases in volume at the sites of the precipitates

300

R. C . NEWMAN AND R . JONES

OY

100

200

300

Anneal Time (h)

FIG.3. The variation of the squared radius of growing precipitates in undoped Cz Si as a function of heating time at 750°C. measured by small angle neutron scattering (SANS), yielding D = 4.4 x lOI4 em's-' (Livingston et al., 1984).

(Bullough and Newman, 1970; Gosele, 1986; Tan, 1986; Taylor, Tan and Gosele, 1991). Values of Doxyhave also been obtained by examining the precipitation process over extended periods of time, which led to the loss of nearly all the oxygen from solution. The oxygen loss AIOi] was measured by 1R spectroscopy with the samples at 4.2 K and the number density of precipitates N was determined by SANS and defect etching (Livingston et al., 1984). N showed only small reductions with increasing anneal time, due to Ostwald ripening, but was very dependent on temperature (Newman et al., 1986a). For a set of samples cut from a particular as-grown boule, not given a prior postgrowth heat treatment, SANS measurements in the exp( + 3 eV/kT) temperature range 650°C to 1050°C led to N = 6 x (Fig. 5): the large increase in N as T was lowered was attributed to the increasing oxygen supersaturation. Conservation of oxygen atoms requires the quantity (4/3)rriNcp to be equal to the loss of oxygen AIOi] from solution at all stages of the annealing. Hence the number of oxygen atoms per particle was also determined for long annealing times (Fig. 6). It follows that the temperature dependence of rp must correspond to that of N i.e., exp( - 1.0 eV/kT) for the set of samples discussed.

8.

30 1

DIFFUSION O F OXYGEN IN SILICON

Somewhat different values would be expected for other samples with different grown-in oxygen concentrations. The important point is that the measured rate of oxygen loss will be given by the product 4 ~ rN, D I O , ] . and will have the temperature dependence of N2'3LI, that is -exp( -0.5 eV/kT), as r, - r,, and the activation energy E, of Doxyis -2.5 eV. Since N was known, the kinetics of the precipitation could be evaluated from least squares fits to the theory of' Ham (1958) to yield values of Doxy (Patrick et al.. 1979; Wada el al., 1980, 1982; Livingston et al., 1984) and the solubility of 0, atoms. c , ( T ) .DC,\? had normal values with El, - 2.5 eV for temperatures down to 650°C (Fig. 4). The values of c, determined

1

1

1

1

I

I

I

I

1

0 REF a

\ 0 HiOx

15~ 1 0 ' ~

Doxy= 0 13exp(-2.53eV/kT)cm2s

0.6

0.8

10

1.2 1OOOiT

1.4

1.6

1.8

(K I )

FIG.4. Arrhenius plot showing the line determined for normal oxygen diffusion (Fig. 2). Also shown are the values of Doh"obtained from the precipitation data of Livingston et al. (1984). who used IR and SANS measurements ( R E F a). the precipitation data of Wada et al. (1980. 1982) ( R E F d), the out-diffusion data o f Gosele et al. (1989) (vertical bars), the oxygen aggregation data of Bergholr et al. (1985) ( R E F b). the thermal donor data of Gaworzewski and Ritter (1981) ( R E F c ) and the oxygenoloss data of Binns (1994). using second-order kinetics and a dimer caplure radius of 10 A ( R E F e). 0, diffusion is clearly the rate-limiting process for precipitation lor 7 2 650°C. but the interpretation at the lower temperature data is still open to dehate.

302

R. C . NEWMAN AND R . JONES

1000 1017-

I

800

'

500

600

'

I

l

l

+

-

I ~

-

0

-

z

-

sr c ._ v)

-

a, c ~

I

FIG.5 . An Arrhenius plot of the number density N of SiOz precipitate particles for a set of samples cut from a common undoped Cz crystal with [O,],= 9 ? 1 x lo" given no postgrowth heat treatment prior to the anneal to induce precipitation (x). Data points ( A ) are for samples cut from a different crystal. These measurements were obtained from 1R and SANS. Points marked ( + ) were derived from IR measurements with the assumption that D,,,was normal (Messoloras et al., 1987).

Temperature ("C) 1 0 9 ~

-

+j107.-

r

. Q m

-

cn

S

c

105-

m L

a,

a

5 z

-

103-

10 8

I

10

I

12

I

14

16

IikT (eV') FIG.6. An Arrhenius plot of the number of oxygen atoms per precipitate particle deduced from the data shown in Fig. 5 (Messoloras et al., 1987).

8.

303

D I F F U S I O N O F O X Y G F N I N SILICON

-

in this way indicated a heat of solution of 1.4 eV at high temperatures but then passed through a broad minimum around 800°C to 700°C (Fig. 7) (Newman, 1988, 1992),due to the increasing importance of the interfacial energy as the precipitate size decreases. Heating for very much longer times, which are not achievable experimentally, should lead to a progressively lower density of larger particles and lower measured values of c J , reflecting the true solubility . In summary. these measurements provided a clear trend for a reduction of the particle sizes as the temperature was lowered to 650°C. The calculated values of c, supported this dependence, were physically meaningful and showed no anomalous behavior. Measurements of the rate of oxygen precipitation at 750°C in silicon highly doped with boron. carbon or antimony (Gupta et al., 1991. 1992a, 1993b) provided no evidence for enhanced or retarded oxygen diffusion. or effects due to changes in the position of E ~ - when , proper account was taken of differences in the number densities and sizes of the precipitate particles resulting from the presence of the second impurity. 3.

OXYGEN

AGGREGATION A T I N 1H:RMEDIAlE TEMPERATURES

At temperatures lower than 650°C. measurements of N by SANS have not been reported because of the lack of sensitivity for detecting small Tmperature ( C)

I

1

6

7

1

8

1

9 10 1 0 4 (K ~

I

I

11

12

I

FIG.7. The measured solubilitv 0 1 oxygen in silicon showing the flattening of the Arrhenius plot near 7 W C , followed by ;in upturn at lower temperatures. which is attributed to the effect of the interfacial energy and implies the presence of very tiny precipitate particles (cf. Fig. 6) (Newman, 1992)

304

R. C . NEWMAN AND R. JONES

SiOz particles (Messoloras et al., 1987). It follows that the number density of diffusion sinks cannot be determined, although values of d [ O , ] / d tcan still be measured. The use of Ham’s equations to analyze the kinetics of the oxygen loss for 500°C 5 T I600”C, with the assumption that Doxy was normal, led to physically unrealistic results, particularly at the lower end of the temperature range when calculated values of N were close to 10l8 ~ m - which ~ , would imply that a growing particle contained only one 0, atom, even at long annealing times. The procedure, or the assumption of normal values of D o x y was , obviously flawed. The capture radius r[ should be given by rc = rp + a , where a is the width of an effective capture zone surrounding the precipitate, which has an actual radius rp. At high temperatures ( T > 650°C) when rp is large we would have rc rp. However, once rp becomes small compared with a , r, would be essentially equal to a and independent of annealing time and temperature. After a rapid initial transient, the kinetics would have the form

-

( c - c , ) / ( c ,- c,)

=

exp( - t / ~ ) , where 7

=

( 4 ~ r D ~ ~ ~ N r( ~ 4 )) - ’ ,

allowing values of N and c, to be determined, again assuming Doxyhad its normal values. This revised procedure leads to an important prediction, not discussed by Messoloras et al. (1987). Since rr was assumed to be independent of temperature, the temperature dependence of d[O,]ldt should be that of the product DoxyN , namely, exp( +0.5 eV/kT). Thus d [ O , ] l d t should show an apparently anomalous increase as T is decreased. This prediction has been verified for samples cut from two boules with different grown-in oxygen concentrations (Fig. 8) (Newman, 1991; Brown, 1991). This result, together with the increasing values of c, as T is lowered in this range (Fig. 7) provide self-consistent evidence that SiO, particles could still grow at a rate limited by normal oxygen diffusion. However, their size was predicted to become very small and at 500°C the number of oxygen atoms per particle was estimated to be only 20 or 30 (Fig. 6). A consequence was that TEM “black dot” contrast was associated with these tiny precipitates. Coherent structures observed by direct TEM lattice imaging and originally assigned to coesite, a high pressure phase of silica would then have to be associated with some other extended defects. Bourret ( 1987) re-interpreted the TEM features in terms of hexagonal silicon, nucleated by the release of I-atoms during the oxygen aggregation. The need to invoke an enhancement of Doxyby a factor of lo4 at 485°C (Fig. 4) (Bergholz et al., 1985) to account for the growth of the “coesite” structure was thereby removed. These authors observed other TEM features that could be attributed to I-atom clusters, implying that these intrinsic defects had been formed. Unfortunately, the conclusions

8.

Temperature ("C) 650 550 450 350

10'

I

l

l

1

305

DIFFUSION OF OXYGEN IN SILICON

I

I

Temperature ("C) lo,316701 570 I 470 I 370

I

Oxyger

- 10'

Oxygen

1 0i7

Slope -0.6eV

-6 . 6

0

Slope

Slope

ij 10'

t u

- 10'

TD . Formation

5 .. T

0

lo9

t a)

1 ne

10

I

12 14 104/T(K')

I

16

lo8 I (b) 10

1

I

12 14 1041 T (K l )

I

16

FIG.8. Arrhenius plots showing the rate of loss of 0,atoms from solution for two b o d e s with ( a ) [O,],, = I .5 x lo'#c m - ' and ( b ) [O,],,= 9 x 10" cm-', respectively. At temperatures 7 2 .SSO"C, the slopes are -0.6 eV and 0 . 3 eV. followed by anomalous rises as the temperalure falls t o -475°C. At lower temperatures the slopes are expected t o become asymptotic to the activation energy for 0,diffusion. due t o the formation of O? dimers but the measured slopes are -1 eV and - I . 3 r V . respectively. Also shown are Arrhenius plots of the rates of formation of TD centers (Brown 1991).

have been confused again by the work of Pirouz et al. (1990) who have argued that the coherent TEM structures are not due to hexagonal silicon and are probably not due to coewe; however, no positive interpretation wa, advanced. We shall return to the subject of heat treatments in this temperature range in Section I V . 3. OXYGEN

AGGREGATION A T L,OW r r E M P E R A T U R E S

( 7 2 S00"c)

Extrapolation of the measurements shown in Fig. 6 to 450°C leads to the conclusion that oxygen loss would occur predominantly by the formation of oxygen pairs O2 up to quite long annealing times. Assuming that 0, defects are stable. we can write d [ O , ] / d r = -87rr,.D[O,]', since any A factor of diffusing 0, atom has a concentration of sinks equal to [Oil. 8 rather than 4 in the equation occurs because the "sinks" are also diffusing. A n analysis of the rate of oxygen loss should yield an activation energy of 1.5 eV, equal to lhat of Dc,xv.according to this mechanism. Measurements led to values o f I ) , , , that were in agreement with normal diffusion at 7 = 420°C and 7' = 450°C (Newman et al.. 1986a) (with r,

306

R. C . NEWMAN AND R. JONES

= 10 A). However, at a higher temperature of T = 500°C the value of Doxy estimated in this way was smaller than the normal value by a factor of -5 (Fig. 4). This result was explained by postulating that dimers would exhibit some degree of dissociation. The total loss of 0, atoms from solution would be smaller than expected from the simplified analysis used, leading to a too small value of Doxy.It would be logical to argue that dimers would become more stable as the anneal temperature was reduced. Meaningful measurements at low temperatures ( T 5 400°C) can be obtained only if the period of the annealing is extended to several thousand hours (at say 350°C) to obtain sufficiently large reductions in [O,].The first such results of Newman and Claybourn (1989) were not reliable and later data implied that calculated values of Doxywere somewhat greater than the normal values at 350°C (Brown et al., 1990a; Newman et al., 1990). Suggestions were made of ways of reconciling these data for long-range migration with those involving single atomic jumps where normal values of Doxywere obtained. It was argued that there may have been in-diffusion of some unknown species such as hydrogen, originating from water vapor in the ambience, but no real evidence for such a process had emerged. Subsequently, many further measurements have been made on samples with differing concentrations of grown-in oxygen (Binns, 1994). It was then found that the calculated values of Doxy increased for anneals at T > 400°C as the grown-in oxygen concentration became larger. This result is qualitatively explicable in terms of dimer dissociation described by

d [ O , ] l d t= -8.rrrcD[0,]2+ k,[O,],

(5)

since the second term would become more important as [O,] becomes smaller. The later data (Figs. 4 and 9) indicate that the measurements for samples with high and low oxygen merge at temperatures below 400°C. There is an implication that dimer formation and dissociation are quite closely balanced, according to these arguments. In that case, the slope of an Arrhenius plot for the rate of oxygen loss (and TD formation) over a limited temperature range would not correspond to an activation energy of a single process: this conclusion is supported by the low temperature data given in Fig. 8. It follows that the determination of the activation energy of Doxy from measurements of the rate of oxygen loss from solution is not a simple procedure. To evaluate numerical values of Doxy,it is necessary to assume a value for the capture radius rcr which should be essentially independent of the temperature. Newman et al. (1986b) argued that this might be as large as 10 A, but Kimerling (1986) thought that the smallest possible value of only 2 A would be more appropriate. We show in Figs. 9 and 10 values

8.

DIFFUIION OF O X Y G E N IN SILICON

307

FIG.9. Arrhenius plots, for furnace annealed samples. o f Dox)determined for low temperature\, according to a model o f stable dimer formation, with a capture raditib of 10 A for two houles with [O,] = 1.5 x 10'" cm ' ( H i Ox) and [ O , ] = 9 x 10" c m - ' ( M E D Ox). respectively. There I S reasonably good linkage to values o f D,>,, determined by stressdichroism measurements. Any enhancement in the rate o f long-range diffusion at 350°C would be no greater than a factor o f 3-4 according to this analysis. The dashed line corresponds to enhanced oxygen diffusion in the presence o f hydrogen (see Figs. I 6 and 17) (Binns. 19941.

of Dolr calculated from second-order kinetics and measured values of d10, Ildr using the two values o f I', to indicate whether or not there might be a linkage to the low-temperature stress-dichroism data. Such a linkage appears quite unreasonable if I', = 2 A but is possible for I', = 10 A . We shall comment further on the choice of this parameter in Section IV when we consider the diffusion of 0,atoms in samples given a prior heat treatment in hydrogen gas (see also Section V1). We simply note that if theory requires I ' ~ - 2 A there is still no implication that Do,) for longrange diffusion at low temperatures (,-,3So"C) is enhanced by more than a factor of about 10. More comprehensive kinetic analyses have been made by Tan et al. (1986) who took the formation of trimets and larger oxygen clusters into account, as well as allowing dissociation of dimers to occur in their model. They also found an apparent increase of Doxywith increasing [O,] but it is difficult to draw further conclusions as the comparison with

308

R. C. NEWMAN A N D R . JONES

FIG.10. Arrhenius plots for furnace annealed samples of Do,, determined for ol! temperatures, according to a model of stable dimer formation with a capture radius of 2 A for two boules with [O,] = 1.5 x lo’* cm-3 (Hi Ox) and [O,] = 9 x lo” cm--’ (MED Ox), respectively. The linkage to values of Doxydetermined by stress-dichroism shows a discontinuity corresponding to a factor of -15 (cf. Fig. 9). The dashed line corresponds to enhanced oxygen diffusion in the presence of hydrogen (see Figs. 16 and 17) (Binns, 1994).

experiments was for one temperature only, namely, 450°C. From measurements of d[O,]ldtalone, it is difficult to determine several parameters ( r , for dimers, r,. for other aggregates, k, for dissociation of dimers, D o x y , etc.) with any degree of precision. We end this section by pointing out that the analysis presented leads to the possibility that Doxyis normal, or only very slightly enhanced, for long-range migration at any temperature from the melting point of silicon down to 350°C. IV. Enhanced Oxygen Diffusion Not Involving Hydrogen

Enhancement mechanisms must involve interactions of Oiatoms with another diffusing species, which may be a vacancy ( V ) , an I-atom or an interstitial impurity that could be a metal such as copper, iron, etc. or nonmetallic carbon, nitrogen or even a second oxygen atom. It is implied that a complex, formed as a transient species, dissociates or is annihilated after a certain time and that one or more 0; diffusion jumps occur as a

8.

DIFFU5ION O F , OXYGEN IN SILICON

309

result of the interaction. We shall first consider interactions with vacancies and I-atoms introduced by 2 MeV electron irradiation. An inherent complication is that the two defects are produced simultaneously, and it has been established that they each form stable complexes with 0, atoms at low temperatures. It is also known that substantial recombination of the two species occurs at 300 K and that part of the process is due to their sequential trapping at 0, atoms (Davies et al., 1987). We have to consider the analyses of oxygen diffusion profiles by SIMS carried out by Shimura et al. ( 1988) for annealing temperatures of 750°C and 1000°C and those of Lee and Fellinger (1986). Lee et al. (1988). and Gosele et al. (1989) relating to temperatures in the range 450°C to 650°C. Effects due to the presence of f-atoms and vacancies were considered in the interpretation of this lattcr work, some of which involved ionimplanted oxygen sources but eventually they were ascribed to rapidly diffusing 0, pairs. The work of Gaworzewski and Ritter (1981) is closely related to these studies. At the end of this section we comment on the effects due to the presence of carbon and metallic contamination. The effects of exposing silicon to hydrogen gas at high temperatures or to atomic hydrogen generated in a hydrogen plasma at much lower temperatures will be discussed separately in Section V .

I . EFFECTS DUETO THE INJECI.ION OF VACANCIES A N D LATOMS B Y 2 MeV ELECTRON IRRAIIIATION Newman et al. (1983a) investigated the effect of room temperature 2 MeV electron irradiation on samples that had been stressed to induce dichroism in the 9 p m band. The irradiation led to the formation of stable oxygen-vacancy pairs (A-centers) that give an 1R absorption band at 836 cm I (77 K ) and a reduction in thc strength of the 9 p m band. There was also a loss of dichroism in the 9 p m band at a rate that depended on the 300°C. For an incident electron flux but not on temperature u p to T this rate (for samples maintained at T current density of 22 p A cm 50°C) corresponded to that for normal 0, diffusion jumps that occur in furnace annealed silicon at a temperature of 350°C. Confirmation that vacancies were involved in the process leading to the enhancement of the loss of dichroism was obtained by irradiating Cz Si doped with isoelectronic tin impurities present in a concentration of 10’’ cm-’. Tin atoms also trap mobile vacancies efficiently to form Sn-V pairs that are stable up to T - 150°C (Brelot, 1973; Watkins, 1975). There was a reduction in the rate of formation of A-centers by a factor of -6 compared with undoped Cz Si because of the competition for trapping the available vacancies and there was a reduction in the rate of l o s s of dichroism in

‘,

-

310

R. C . NEWMAN A N D R. JONES

the 9 pm band by the same factor (Oates et al., 1984). However, if the sample temperature were raised above 150°C during the irradiation, so that tin atoms no longer trapped vacancies to form stable Sn-V pairs, the rates of formation of A-centers and the loss of dichroism were the same as those measured in undoped samples irradiated at room temperature. The capture of a vacancy by an 0;atom could produce a diffusion jump due to the rapid re-orientation within the A-center (Watkins and Corbett, 1961) followed by either (a) its dissociation or (b) by the capture of a mobile I-atom, so that the final bonding of the Oi atom was to different neighbors from the original neighbors. Newman et al. (1983a) concluded that A-centers captured mobile I-atoms, in agreement with the model of radiation damage discussed by Davies et al. (1987). An alternative possibility that 0; atoms first captured a mobile I-atom and then a vacancy, which could also lead to a diffusion jump, was discounted, as O i l complexes have a small binding energy and they are formed only during irradiations below room temperature (Section IV.2). When undoped prestressed Cz Si was irradiated at temperatures above T - 300"C, A-centers were not detected in IR spectra, which was not surprising in view of their known annealing at these temperatures (Svensson and Lindstrom, 1986). Nevertheless, the rate of loss of dichroism increased dramatically (Oates, Newman and Tucker, 1985) and the possibility had to be considered that A-centers were produced as a transient species and that one or more diffusion jumps occurred before dissociation. Oates and Newman (1986) initially inferred that dissociation did occur by demonstrating that the loss of A-centers during an isochronal annealing was accompanied by a corresponding increase in the concentration of unpaired 0;atoms. However, later work showed that regeneration of isolated 0;atoms occurred only in samples that had been given a large (-5 X 10l8 cm-2) dose of 2 MeV irradiation and then only in the first stage of an isothermal anneal (Newman, Tipping and Tucker, 1986b; Svensson and Lindstrom, 1986) (Fig. 11). Dissociation of a complex cannot suddenly stop at some stage during an annealing, and so Newman et al. (1990) argued that the initial loss of A-centers occurred by the capture of I-atoms released from clusters of these defects that had also been formed during the extended irradiations. In the second stage of the annealing (Fig. 1 I ) , conversion of A-centers to another type of defect that gives IR absorption at 889 cm-' at 300 K (894 cm-l at T 5 77 K) is observed. The general consensus is that this defect should be assigned to an 0,-V complex (Corbett, Watkins and McDonald, 1964b) that is produced when a mobile A-center diffuses to an uncomplexed 0; atom. However, this interpretation has some shortcomings. During the forma-

8.

DIFbCI\IC)N O F O X Y G L N IN SILICON

311

Loss of iritegiated absorption from

the 835cm ' A band (cm ,')

FIG. I I . The loss in the integrated abwrption ( I A ) coefficient of the 835 c m - ' 1K line fi-om 0,-1' pairs (A-centerh) during an isothermal annealing of a sample at 300°C. following 2 MeV electron irradiation at room temperature to a dose of 6 x 10IKcm-:. In stage 1 the lost absorption reappears a s an increase in (he IA of the 9 pm 0, band. At a later stage (11) this process terminates. and there i h correlated growth of a line at 889 c m - ' (O?-V center) ( N e w m a n et al.. 1986b. 1990).

tion of 889 c m - ' defects there is no further loss of 0, atoms from solution (Svensson and Lindstrom, 1986; Newman et al., 1986b; Stein, 1986). In addition, there is no isotopic splitting of the LVM corresponding to Ih 0 I 8 0 V centers in samples containing the mixed oxygen isotopes (Stein, 1986; Abou-el-Fotouh and Newman, 1974). Finally, the effects of an applied uniaxial stress have shown that the defect symmetry is lower than the commonly assumed Dz,,(Bosomworth et a]., 1970). In spite of these uncertainties, it seems that the 889 c m - ' defect must incorporate at least one lattice vacancy. In that case, the fact that the defect is not generated in t h e early stages of the annealings of highly irradiated samples (5 x 10" cm ' 1 can be explained (Fig. 1 I ) . If I-atoms are released from large aggregates of the defects and are trapped by A-centers. they could also be trapped by the 889 c m - ' defects so that no detectable concentration builds up. At a later stage in the annealing. the flux of released I-atoms would he reduced but not to zero; thus there could be some continued annihilation of A-centers to regenerate 0, atoms. while simultaneously. other A -centers migrated to 0, atoms to form new 889 c m - ' defects leading to a loss of 0, atoms. Svensson and Lindstrom (1986)had to argue that there was a hularice of such processes to explain their observation that 10,] remained constant during stage 11 of the annealing. For low-irradiation doses ( 2 x lo" em-') only small

312

R. C. NEWMAN A N D R. JONES

aggregates of Z-atoms would be formed. If these clusters were relatively unstable and dissociated at the beginning of the annealing it is possible that there would be immediate formation of 889 cm-' defects as found by Newman et al. (1990); that is, stage I of the annealing was not detected (Fig. 1 1 ) . Further work is required to clarify the interpretation of the observations. The most important point to emerge is that there is no evidence for vacancy-enhanced diffusion of Oi atoms at temperatures below -300°C. The 889 cm-' defect is stable up to T 450"C, while at higher temperatures, aggregation of Oi atoms occurs and the diffusion rate is normal (Section 111.1).

-

2. THEEFFECT OF EXCESS Z-ATOMS It has been suggested that the presence of Z-atoms alone enhances Doxy (Ourmazd, Schroter and Bourrett, 1984). The irradiation experiments discussed previously provide no supporting evidence for this process but, on the other hand, they do not lead to its exclusion. From the measurements on the tin doped silicon it can be deduced that any direct enhancement of Doxyby Z-atoms is smaller by a factor of -6 than that arising from the recombination of Z-atoms with A-centers. In an earlier work, Brelot and Charlemagne (1971) showed that 0;atoms formed complexes with 1-atoms generated during low temperature (77 K) 2 MeV electron irradiation of Cz Si. This result is analogous to the formation of 0;complexes with interstitial carbon atoms (C;), which have been called C(3)centers (Davies and Newman, 1994). The latter defect is stable up to T 350°C (Ramdas and Rao, 1966) but the Oil defect that gives IR LVM lines at 956 cm-I, 944 cm-' and 935 cm-' (Brelot and Charlemdgne, 1971) dissociates near 50°C. The release of Z-atoms is unambiguous since they are retrapped by substitutional carbon impurities that are ejected into interstitial sites. Brelot (1972) determined an activation energy for the dissociation of O i l defects by carrying out an isothermal anneal at 333 K for a limited time, after which the sample was given further heat treatments at 348 K. From the measured tangents of the curves for the anneal of the 935 cm-' IR line at the point where the temperature was changed (Fig. 12), he determined Edlsof -1.0 0.1 eV. This energy should be the sum of the binding energy EB and the migration energy EM of the Z-atoms. He assumed that E M 0.2 eV to obtain EB 0.8 eV. These measurements lead to the view that Doxymight be enhanced due to the presence of Z-atoms and the activation energy would be (EF - EB + E M ) ,where EFis the formation energy of an Z-atom. For the formation of 1-atoms by a thermally activated intrinsic process, EF would be very

-

*

-

-

8.

10

313

D I F ~ U S I U NOF O X Y G E N I N SILICON

20

30 Anneal time (rnin)

0

4

0

FIG.12. Reduction in the strength o f the absorption coefficient of an 1R line at 935 c m - l ( 0 - 1 pairs) during an isothermal annealing at 333 K for up to 37 rnin. followed by further isothermal annealing at 348 K. leading lo a dissociation energy of 1.0 eV; the assumption that the migration energy of an /-atom I \ 0 2 eV leads to a binding energy of 0 8 eV (Brelot. 1972)

large ( - 5 e V ) but there is evidence that f-atoms are generated during the aggregation of 0, atoms at high temperatures when stacking faults and other defects grow adjacent to SiOZ precipitates (Bourret, ThisbaultDesseaux and Seidman, 1984). The initial rate of I-atom generation would then be controlled by the rate of loss of oxygen from solution for which the slope of an Arrhenius plot is quite low (Fig. 8). If f-atoms were similarly generated at low temperatures ( T < 500°C) this energy might rise to the activation energy of normal oxygen diffusion (2.5 e V ) , leading to a mechanism of enhanced diffusion of remaining isolated 0, atoms with activation energy of about 1.9 eV. The contribution of this process to the total diffusivity would depend on the concentration of f-atoms present. Newman et al. (1983a)argued that one /-atom is generated for every two Oi atoms that coalesce, even at these low temperatures (see also Section VII), but the rate of loss of uncomplexed f-atoms from a crystal is uncertain. and so it is not possible to estimate a concentration arising from a dynamic equilibrium between the two processes. Although substitutional carbon atoms are efficient traps for mobile I-atoms (Newman et a]., 1983a). the rates of loss of 0, atoms from solution in (a) carbon-free loi8 cm ~’are material and (b) material containing carbon with [C,] essentially equal. The latter measurements therefore provide no evidence

-

314

R. C . N E W M A N AND R. JONES

that the presence of I-atoms generated by the internal aggregation of Oi atoms enhances Doxy.Small variations in Doxyhave been observed, but these can be correlated with differences in the grown-in oxygen concentration (Tan et al., 1986; Newman and Claybourn, 1989) (see Section VII). In summary, enhancements of Doxywould be expected at low temperatures if mobile I-atoms were present but experimental evidence supporting this mechanism is essentially nonexistent. It could be inferred that this lack of evidence implies that the formation of I-atoms does not occur. There is a possible exception to this negative conclusion. In Section 111, it was shown that values of Doxydetermined from oxygen loss measurements at very low temperatures appear to be somewhat greater than those determined from stress-dichroism measurements. We point out that even if there were I-atom formation in the extended annealing required to measure the oxygen loss, no I-atoms would be generated during the short heat treatments required to effect single 0;jumps. Although discussion of these particular low temperature measurements has already been deferred, it is necessary to consider yet additional evidence, in relation to Si containing hydrogen impurities (Section V), before the discussion can be completed.

3. RAPIDDIFFUSION OF DI-OXYGEN DEFECTS In Section 111 it was assumed that stable immobile oxygen pair defects are formed during annealings at T 5 450°C. Various models for these defects have been proposed as a result of theoretical analyses, and it is concluded that there is a binding energy (Section VI.5). IR absorption from these defects has not been detected, either as LVM lines at frequencies different from those of isolated Oi atoms, or from modifications of the lines from the latter centers (Brown et al., 1990b). If two 0, atoms were present at adjacent Si-Si bonds with a common apex, the frequency of the 1136 cm-' Oi band (4.2 K) should be shifted. Second, the rotational motion about the [ 1 I I] bond axis should be quenched or severely modified. Changes in the rotational energy levels would be detected by making IR absorption measurements at T 10-20 K when the first excited rotational state is occupied (Bosomworth et al., 1970). Brown et al. (1990b) compared the spectra of heated and unheated samples but found no detectable difference. It has been stated by Stavola and Snyder (1983) that they made similar measurements, but again no differences were detected. Possible inferences of these negative results are that if close oxygen pairs form there are large changes in the local bonding so that the oxygen vibrational modes are shifted away from the 9 p,m region or the pairs are lost from solution by rapid diffusion to traps.

-

8.

DIFFUSION O F O X Y G E N IN SILICON

315

Rapid diffusion of di-oxygen "molecules" was proposed by Gosele and Tan (1982). who supposed that pairs of these defects combined to form 0, complexes. However. no detailed atomic structure was proposed for either the O2 or the 0, centers, and neither was the mechanism of the rapid diffusion of 0, explained. The main feature was that the model offered an explanation for the results of Kaiser et al. (19581, who found that the rate of formation of TD centers was proportional to 0:. Recently, 1,ondos et al. (1993) have shown that this power dependence is specific to an annealing temperature of 450°C and for T I 400°C, the rate is proportional to 0:. At these lower temperatures estimates of Doxy,determined from the rate of oxygen loss and the use of second-order kinetics, become independent of the grown-in oxygen concentration. Hence the relevance of the idea of Gosele and Tan (1982) to TD formation is now less obvious since it could be inferred that a TD center contains only two oxygen atoms. In a later work Giisele et al. (1989) again invoked the presence of rapidly diffusing O2 dimers to explain the SIMS measurements of Lee and Fellinger (1986) and Lee et al. (1988), which indicated rapid mass transport of oxygen out of surface regions of Cz crystals heated in the range 500°C to 65OoC, with enhancements of Doh).by factors of up to 10' (Fig. 4). Related SIMS measurements showing rapid in-diffusion of oxygen. ( I x 0 ) . from surface souIces produced by ion implantation were also explained in this way. The interpretation of the latter measurements may not be straightforward because of the large amount of lattice damage that would have been produced by the implantation and the observations that the presence of damage can lead to enhancements of Doxy(Section l V . I ) . In their analysis, Ciosele et al. (1989) postulated that there were two types of oxygen dimers. The first consisted of a pair of adjacent oxygen atoms that was highly mobile and could dissociate, while the second, 0;. was formed when an /-atom was ejected, so that 0: was considered to correspond to the first stage of precipitation. The emission of /-atoms was considered necessary to account for the family of TD centers that was formed for T < 500°C (see Claybourn and Newman, 1987). N o alternative explanation has been proposed for the anomalous SIMS data and so it would be imporiant for the measurements to be repeated. Superficially. the results of Gaworzewski and Ritter (1981) appear to bupport the rapid out diffusion of oxygen at 450°C. They estimated an enhancement factor of 10'' (Fig. 4) by measuring the depth profiles of thermal donors. However. if T D centers incorporate some other component such as an /-atom, these measurements could relate to the outdiffusion of that component rather than oxygen.

-

316

R. C . NEWMAN AND R. JONES

4. EFFECTS DUETO CARBON

Shimura et al. (1988) reported SIMS measurements of the out-diffused profiles of oxygen from Cz Si wafers heated for 64 hours in dry oxygen, either at 750°C or 1000°C. The oxygen concentrations were [O,] = 1.13 x lo’* ~ 1 7 (according 1 ~ ~ to the calibration of Baghadadi et al., 1989), and the crystals contained either a low carbon content, L(C) < 5 x loi5~ m - ~ , or a high carbon content, H(C) = 4 x 1017~ m - Heating ~ . a L(C) sample at 750°C led to negligible oxygen precipitation as determined from 1R measurements, while the out-diffused SIMS profile was stated to be “fairly in agreement” with that calculated from Eq. (3) using the normal value of Doxy(Table 11). In our opinion, the agreement was excellent. The validity of the measurement techniques was thereby established and Doxywas normal. After the L ( C ) sample had been heated at IOOO’C, the calculated outdiffused oxygen profile ran parallel to that measured by SIMS but was lower in concentration by a factor of -2. There was a similar but larger discrepancy for the H(C) sample heated at 1000°C. It was inferred that the oxygen diffusion was retarded by the presence of I-atoms generated by the internal precipitation of 50% ( L ( C ) )and 86% (H(C)), respectively, of the grown-in oxygen and by the formation of additional I-atoms at the surfaces due to the growth of SiO, layers (Shimura 1991). It was then argued that these results supported a vacancy mechanism for oxygen diffusion, as proposed by Heck et al. (1983). However, the use of Eq. (3) is not appropriate for the analysis of these samples as the precipitated oxygen would not be mobile and could not contribute to the out-diffusion although it would still be detected by SIMS. A more complex calculation is required to analyse the data before it could be concluded that Doxydid not have its normal value. On the other hand, the result of heating a L(C) sample at 750°C was interesting and could be important. This sample showed losses of oxygen of 9.3 x 1017 ~ r n and - ~ all the carbon atoms, 4 x 10” ~ m - from ~ , their normal lattice sites, and the formation of complexes involving interstitial carbon (C,) and two or more 0, atoms (C,O,n),which were designated as perturbed C(3) centers (Shimura, Baiardo and Fraundorf, 1985; Shimura, 1986). The relevant feature to the present discussion was the observation of enhancement in Doxyfrom the normal value of 4.47 x 10-l4 cm-, SKI to 1.51 x cm2 s-I and the diffusion coefficient of carbon was also enhanced. The latter effect can be understood as substitutional carbon atoms would be ejected into interstitial sites by the capture of Z-atoms and the resulting C, atoms have a high diffusion coefficient, D = 0.44 exp(-0.87 eV/kT) cm2 s - I (Tipping and Newman, 1987). It was then

8.

DIFFU\ION O F OXYGEN IN SILICON

317

proposed that C,-Oi complexes have a higher diffusivity than isolated 0, atoms, similar to the proposal that (0,). defects might also have a higher rate of diffusion (Gosele and Tan, 1982). It is interesting that 1R data for the unperturbed C(3) center imply that the oxygen atom is displaced from its normal bond-centered site (Davies et al., 1986) and this displacement is also predicted by uh initio calculations (Jones and Oberg, 1992). In summary. it has been shown that a heat treatment of L ( C ) material at 750°C in dry oxygen, which would lead to the injection of excess /-atoms at the surface, still led to a diffused oxygen profile with a normal . contrast, the presence of grown-in carbon led to envalue of D o x yBy Iiuticc~dout-diffusion of oxygen. with the implication that the presence of interstitial carbon atoms leads to the formation and rapid diffusion of O,C, complexes. I t is important to note that there was no enhancement during an anneal of a H ( C ) sample at I00o"C. but that 1R measurements then failed to reveal CiO,,,complexes. which are presumably unstable at the high temperature.

5.

EFFECTS D U E .TO

METALLIC. C O N 1 A M I N ATION

I t is well known that tranhition metals such as Ni, Fe and Cu diffuse rapidly in silicon as interstitial species. Consequently, transient complexes with 0; atoms could he produced, leading to a n oxygen diffusion jump upon dissociation. The experimental work of Newman. Tipping and Tucker (1985) and Tipping et al. ( 1986) appeared to support this view. Fe or Cu was diffused into Cz Si at 900°C and subsequently enhanced diffusion jumps were observed i n measurements of the relaxation of stressinduced dichroism. The transfer of Cu atoms from substitutional to interstitial sites during cooling from the 900°C treatment and the production of vacancies was also considered to be important. Woodbury and Ludwig ( 1960) found that vacancies formed by this process led to site switching of interstitial Mn impurities to substitutional sites. The possibility that the presence of vacancies might lead to enhanced oxygen diffusion has been discussed and shown nut to be very likely. In the work of Tipping et al. ( 1986). the metallic impurities were introduced by heating silicon in contact with their hydrated salts (nitrates),and the presence of hydrogen (Secimpurities would almost certainly have led to enhancements of Doxy tion V ) . Nevertheless the metals may have played a secondary role as will be explained in Section V . 3 . 6. SUMMARY

It has been shown that irradiation damage, involving the sequential capture of vacancies and then /-atoms by 0, impurities enhances D o x y .

318

R . C . NEWMAN AND R . JONES

The injection of vacancies or I-atoms alone could also lead to enhancements but their magnitudes cannot be estimated and there is no clear experimental evidence to support these mechanisms. Likewise, the presence of fast diffusing metallic impurities could enhance Doxybut again there is no supporting experimental evidence. It has been shown that the presence of grown-in carbon leads to enhanced out-diffusion of oxygen at 750"C, possibly due t o the rapid diffusion of CiOicomplexes. However, measurements were reported only for one sample and further work is needed to verify the result. This leaves hydrogen as the dominant catalyst (Section V), with the additional possibility that 0, centers diffuse more rapidly than isolated 0; atoms (Section VIII). The lack of experimental evidence for the existence of O2 centers in heated samples could support this view. If 0, centers do diffuse rapidly there are important consequences relating to the formation of TD centers for T < 500"C, and the rates of oxygen loss from solution in the range 500"C-600"C (see Section Vll). V. Silicon Containing Hydrogen Impurities Fuller and Logan (1957) found that the rate of TD formation in Cz Si grown in an atmosphere of hydrogen was ten times greater during subsequent heat treatments at 450°C than that in material grown in the same equipment but in a helium atmosphere (Fig. 13). It has now been demonstrated from electron nuclear double resonance (ENDOR) measurements made on Si containing enriched "0 (Michel, Niklas and Spaeth, 1989) (Chapter 6) that TD defects incorporate small oxygen clusters. The measurements of Fuller and Logan therefore provided the first evidence that long-range enhanced diffusion of oxygen can occur during oxygen aggregation at low temperatures. Previously van Wieringen and Warmholz (1956) showed that hydrogen may be introduced into Si by heating crystals in hydrogen gas to temperatures close to 1200°C. Diffusion occurred throughout material with a thickness of -1 mm, the solubility was -10'' ~ m - and ~ , the activation energy for diffusion was estimated to be -0.5 eV. The validity of extrapolations to low temperatures ( T < 500°C) is unclear because of (a) the formation of complexes of hydrogen with impurities and defects, and (b) the likely formation of H, pairs and perhaps larger hydrogen clusters. Recently, the effects of the presence of hydrogen, introduced into Cz silicon by high-temperature annealings in H, gas, on the long-range diffusion of 0;atoms during subsequent annealing at T 5 500°C has been examined (Section V. 1). Alternatively, hydrogen may be introduced as the atomic species at low temperatures by exposing samples to a hydro-

8.

1

319

DIFbtISION O F O X Y G E N IN SILICON

100

10

1000

Anneal time (h) F I G . 13. A compariwn of the introduction rates of added electron carriers. from resislivitv measurements, due to the formalicin of thermal donors for two Cz silicon crystals. ( a ) grown i n H, gas, and (h) grown in He gas in the same puller, showing the enhancement due to the presence o f hydrogen (Fuller. and Logan, 1957).

gen (or deuterium) RF plasma (13.56 MHz, 50 W, 1-2 Torr) (Section V.2). 1.

SIL.I(.ON

HEATED IN

HYDRO(iEN

GAS

McQuaid et al. (1991) demonstrated that samples preheated in H, gas at 900°C for 2 hrs and quenched to room temperature, showed enhanced rates of relaxation of dichroism of the 9 pm band following an intermediate stressing treatment at 420°C. An Arrhenius plot (Fig. 14) for the range 250°C 5 T 5 350°C indicated that Do,.).had a reduced activation energy of -2.0 eV, in agreement with the earlier measurements of enhanced oxygen diffusion (Stavola et al., 1983) for which there was no adequate explanation at that time. The samples used in the latter work had also been given a postgrowth treatment at 900°C for 2 hrs that was carried out in the crystal growing chamber in an atmosphere of argon-hydrogen (Kimerling. private communication). The introduction of metallic impurities would have been avoided (Section 1V.4). but the presence of hydrogen gas in the ambience was a common feature of the two investigations. By measuring the concentration of passivated H-B pairs in quenched Si samples by precalibrated 1R LVM spectroscopy, McQuaid et al. ( 1991. 1992, 1993) and Veloarisoa et al. (1991, 1992) showed that the concentration of dissolved hydrogen increased monotonically in the range 900°C to 1300°C up to c m - j (Fig. IS). McQuaid et al. (1991) also demon-

320

R. C. NEWMAN AND R. JONES

FIG.14. Arrhenius plots of Doxyshowing normal diffusion (dashed line) and enhancements with a lower activation energy (-2 eV) for samples preheated in H2gas at various temperatures in the range 600”C-1250”C, followed by a rapid quenching to room temperature. The measurements were made by the relaxation of stress-induced dichroism. N . B . : The enhancements increase up to a quenching temperature of 900°C but then saturate (Newman et al., 1992).

strated (a) that the H-B pairs were distributed uniformly throughout Samples -1 mm in thickness and (b) that the hydrogen originated from the gas, since replacing H, by D , led to the formation of D-B pairs but not H-B pairs. The concentration of [H-B] pairs saturated for a given heat treatment as the concentration of boron was increased beyond lo” ~ m - ~ . These data have now been confirmed by direct SIMS measurements made on both boron doped and undoped deuterated material and “hidden” (non-IR active) hydrogen has been revealed (McQuaid et al., 1993). The presence of hydrogen in n-type quenched silicon (Veloarisoa et al., 1991) can be revealed by subjecting samples to 2 MeV electron irradiation but pairing of hydrogen with phosphorus impurities in such material was not detected. Thus, two independent groups have shown that hydrogen dissolves in silicon at high temperatures but further work is required to determine the solubility because of the recent detection of hidden hydrogen. Nevertheless, the numerical data are close to those of van Wieringen and Warmoltz (1956) and Ichimiya and Furuichi (1968) (Fig. 15) but the validity of extrapolations to temperatures below 500°C is again unclear.

8.

32 1

DIFFUSION OF O X Y G E N IN SILICON

The effect of using different initial hydrogenation temperatures on the subsequent rate of oxygen diffusion jumps was examined by Newman et al. (1992). Samples quenched from 600°C showed enhancements in Doxy but only for annealings at T 5 325°C. Increasing the temperature of the pretreatment up to 900°C led to increases in D o x y ,consistent with an increase in t h e pre-exponential factor, Do (Fig. 14). Further increases of the pre-annealing temperature to 1250°C led to no further increase in D o x y . This result was surprising in view of the measured increasing hydrogen solubility in this temperaturf, range, since it had been proposed that the presence of atomic hydrogel1 was responsible for the enhancement. It should be pointed out, however, that the effects of the intermediate heat treatment at 420°C required to induce the dichroism are not fully understood. Tipping et al. (1986) have shown that the cooling rate from 420°C has a large effect on measured enhancements of Doxythat are small if the rate is either very high or very low. In addition, the enhancement is sometimes found only as a transient effect, depending on the procedure adopted (Brown et al., 1990b). Other samples heated at 1300°C in H, gas and quenched to room temperature have been annealed at temperatures in the range 325°C 5 7' 5 Temperature ("C)

-

0.6

07

0.8

09

1000 i T (K.')

FIG. IS. Measurements of the solubility of hydrogen in silicon obtained by heating samples in hydrogen gas. quenching to room temperature and measuring the concentrations of H-B pairs (H. 0 and solid line. McQuaid et al., 1992). Also shown are the permeation data ( + 1 of van Wieringen and Warmolrr (1956) and ( x and dashed line) measurements relating to tritium radioactivity of Ichimiya and Furuichi (1968). Figure taken from McQuaid et al., (1997).

322

R. C. NEWMAN AND R. JONES

Temperature (“C)

N

10-2’ -

-

A

Dichroisrn

w

ME DO^ 0.9x

1018

A LoOx 0.65 x

cm 3 cm-3

\\\\

‘\\ \

I 0-23 1.2

I

I

1.4

I

I 1.6

I

\\.

I

1.8

103 i T (K-’)

FIG.16. Arrhenius plot of Doxy (enh), determined from a model of stable dirner formation with a capture radius of 10 A for samples quenched in H2 gas. There is a clear linkage to values of Do,, determined by the stress dichroism technique leading to Do,, (enh) = 2.3 x exp( - 1.7 eV/kT) cmz s-I (cf. Fig. 9) (Binns, 1994).

470°C to determine the rate of oxygen loss from solution (Binns, 1994). Values of Doxywere calculated on the basis of second-order kinetics, assuming that there was no dissociation of (0i)2 pairs. The results are shown in Figs. 16 and 17, with the assumption of capture radii of 10 A and 2 respectively, as used for the analysis of furnace annealed samples (Section 111.3). The values of Doxyso obtained were all enhanced, as can be seen from the diagrams where the dashed line shows normal oxygen diffusion. There was an overlap in the temperature range used for these samples with the range used for the dichroism measurements for which the quenching temperature was 1200°C. If the capture radius was set equal to 10 A there was continuity between the two sets of data exp( - 1.7 eV/kT) cm2 S K I over the leading to Doxy(enh) = 2.3 x range 275°C to 400°C so that the value of ED was somewhat lower than that derived from the stress-dichroism data alone. However, large errors are expected because of the limited temperature range used. For r, 2 A there is a discontinuity between the two types of measurements (Fig.

A,

-

8.

323

DIFFII\ION O F O X Y G t N I N SILICON

Temperature ("C)

Assumed capture radius rc = 2A

8

10"

-

A

Dichroisrn

A LoOx

0 65

10"cm

'\ \

1

1023

1.2

1 14

I

I

I

1.6 10' / T (K ' )

'.

I 1 .a

FIG. 17. Arrhenius plot off),,, ( r n h ) determined from a model of stahle dirner formation with a capture radius of 2 A for samples quenched in HIgas. There is a discontinuity to values of D,,,, determined by the sire\\ dichroism technique icf. Fig. 16) (Binns, 1994).

17). In these samples, any small enhancement effects that might have been produced in furnace annealed samples for long heating times would have been completely overridden because of the hydrogen pretreatments. I t would seem, therefore, that a choice of Y 10 A has to be made to obtain self-consistency, if the analysis of di-oxygen formation is valid.

-

3. SILICON HEATED IN

AN

R F PI.ASMA

Prior to the work on quenched samples, measurements had been made on Cz Si that had been treated in an inductively coupled radio-frequency hydrogen plasma ( 1 Torr, 40 W . 13.56 MHz) (Brown et al., 1988, 1990a; Murray, Brown and Newman, 1989; Newman et al., 1990, 1992). The rate of thermal donor formation was increased for sample temperatures in the range 250T-4So"C and there were enhanced rates of (a) formation of carbon-oxygen complexes. (b) loss of Oiatoms from solution, and (c) loss of substitutional carbon in magnetic Czochralski (MCz) crystals. It

324

R. C. NEWMAN AND R. JONES

was known that the plasma treatment leads to the introduction of atomic hydrogen at the low temperatures used, because of the formation of passivated H-B, H-A1, H-Ga, H-P, H-As, H-Sb pairs etc. in doped crystals (Stavola and Pearton, 1991). Consequently it was inferred that the presence of hydrogen led to enhancements in Doxy. Enhanced rates of loss of dichroism were then demonstrated. Initially, it was supposed, erroneously, that the process occurred uniformly throughout the total thickness ( 2 mm) of the samples (Newman, 1990). Later, it was recognized that it would take time for the hydrogen to diffuse into the silicon and that this time scale might be comparable with the time intervals used for the measurements of the loss of dichroism. These ideas were shown to be correct by Newman et al. (1991), who found that the dichroism was lost rapidly in surface regions of samples but not in their interior. The thickness of the surface region increased with the time of heating and allowed estimates to be made of the depth to which the hydrogen diffused as a function of time. These data led to values of an effective diffusion coefficient for hydrogen in this lowtemperature range, but the nature of the diffusion process was unclear and was almost certainly trap-limited (see, for example, Leitch et al., 1 992). Heat treatments were also carried out in deuterium, helium, argon, argon-oxygen and nitrogen plasmas. Enhancements of Doxywere found only when deuterium was used or if the nitrogen was deliberately contaminated with water vapor (Fig. 18). Plasma treatments were also extended to long times and enhanced rates of oxygen loss and thermal donor formation were found. Enhancement factors of -5, 30 and 200 were found at 45OoC, 400°C and 350"C, respectively (Murray et al., 1989). These observations were consistent with independent studies of TD formation made by spreading resistance measurements by Stein and Hahn (1990a, 1990b, 1990c, 1992) to determine the depth profiles (Fig. 19). These workers also investigated the formation of TD centers in Cz Si beneath buried SiO, (SIMOX) or Si,N, (SIMNI) layers. Enhanced rates were found for the former samples, but not the latter. It is known that SiO, is permeable to hydrogen but Si,N, is not, when the thickness exceeds -100 A (Chevallier et al., 1991). It is clear from all the experimental data that hydrogen plays a key role in the process leading to the enhancement of Doxy. 3 . AN OUTLINE MODELAND SUMMARY

Estreicher (1990) put forward a model whereby H-atoms diffused rapidly in the Si matrix and made random collisions with 0; atoms. It was

8.

325

D I F F t I \ I O N O F O X Y G E N IN SILICON

Anneal time (h)

FIG.18. Thermal donor formation in uiidoped C r Si heated at 400°C in nitrogen plasmas with increasing water vapor content and comparison with ii furnace heated sample and another heated in a hydrogen plasrna (Newman et al.. 1991).

5 After a hydrogen plasma anneal C

0 ... E

c

C a 0 0 0 L

a, L

rc 0

Background doping level

0

100

200 300 Depth iprn)

400

500

t i c , . 19, Thermal donor profile measured by spreading resistance for n-type silicon sample\ with (O,l0= LO" cm-' heated in a deuterium (or a hydrogen) plasma for 2 hrs at 400°C. illustrating the limited depth of the deuterium diffusion (Stein and Hahn, IY90bl.

326

R. C. NEWMAN AND R. JONES

assumed that close 0-H pairs formed as a transient species and that a diffusion jump of the 0,could occur when the complex dissociated. Thus the hydrogen acted only as a catalyst. The probability per unit time P of a collision with one 0, atom is P = 4rC.rrD,[H], where rc 5 A is the interaction radius. It was then assumed that Doxy(enh) = Pd’, where d is the oxygen diffusion jump distance. If both D, and [HI were known, it would be possible to calculate Doxyfor this model which presumes a spontaneous diffusion jump of 0,.The permeation measurements of van Wieringen and Warmoltz (1956) yielded a value of 2.3 eV for the sum of the activation energy of D, and the heat of solution of atomic hydrogen. The activation energy of Doxy(enh) should then be equal to this value. However, if there were a binding energy for the pair (Newman et al., 1991) (see Section VI), this estimate should be reduced and might give a value consistent with the experimental value of 1.7 to 2.0 eV, although the validity of extrapolations from high to low temperatures has already been questioned. Finally, we comment that there may have been some metallic impurities (copper) in the as-grown material and further limited amounts of contamination may have been introduced during plasma treatments. There is no evidence that fast diffusing metallic impurities lead directly to enhancements in Dpxy but it has been proposed that the presence of copper catalyzes the dissociation of H, (tritium) molecules in Ge crystals so that the concentration of atomic hydrogen is increased (Hansen, Haller and Luke, 1982). If the same process occurred in Si, indirect enhancements of Doxycould also result (Newman et al., 1991).

-

VI. Theoretical Modeling of Oxygen Diffusion

In spite of the colossal number of experimental studies of oxygen aggregation in silicon, there have been comparatively few fundamental theoretical studies of oxygen complexes and their migration. In part, this is because of the complexity of the problem. One needs a method that is capable of describing the way in which 0 atoms push themselves into Si-Si bonds, enlarging and possibly breaking them. The method must also be able to handle 0-vacancy, Oi-Oi and 0,-self-interstitial interactions as well as saddle-point geometries where over- and undercoordinated oxygen and silicon atoms might exist: some of these defects have gap levels and might diffuse as a charged species. It is clear that empirical interatomic potentials that have been developed for a number of isolated defects cannot be relied on to predict, with confidence, the properties of these oxygen complexes. Instead one requires a method that solves the many-body Schrodinger equation for the electrons and nuclei, within the

8.

DIFFUSION O F OXYGEN I N SILICON

327

Born-Oppenheimer approximation, computing the total energy and then moving the atoms until this energy is minimized. It is only recently that efficient methods of dealing with this Schrodinger equation and the substantial computational resources they require have become available, as discussed in Section VI. I . In Section VI.2 we describe reaction rate theory that is at the heart of any calculation of 0 diffusion at temperatures much lower than barrier heights. We then describe in Section V1.3 results that have been obtained for interstitial oxygen. 0 , ,including its activation energy for a diffusion jump to an adjacent bond centered site, and in Section V1.4 how the presence of atomic hydrogen can catalyze this motion. The first stage of oxygen aggregation probably involves a pairing of two 0, defects. This does not result in an oxygen molecule but an Si-0,Si-Oi-Si unit. Its structure and binding energy is contentious, and there is only one work that describes its diffusion, as discussed in Section V1.5. Finally, in Section V1.6 a discussion is given of several other oxygen complexes. 1. THEORETICAL METHODS

The two standard methods of calculating the energy and structure of a defect by solving the many-body Schrodinger equation are based on Hartree-Fock (HF) and local density function (LDF) theories (Lundqvist and March, 1986; Ihm, 1988). ‘They are not devoid of approximations and assumptions but they have been found to be particularly useful for ground-state molecular and crystalline structures. They are both variational procedures with H F theory assuming the wavefunction to be the variational variable whereas LDF theory, applicable only to nondegenerate ground states. takes it to be the charge density. The former variable is a function of the coordinates of all the electrons whereas the latter is a function of just three coordinates. In the spin-polarized version. the variational variables include the magnetization density. Both theories can be written in terms of single-particle Schrodinger equations with the potential acting on an electron arising from an effective field due to all the others. Thus both require a self-consistent equation to be solved. However there are important differences-especially in the treatment of exchange and correlation. HI; theory ignores the latter and its inclusion i.ia, say, Moller-Plesset perturbation theory is unwieldy. LDF theory includes an exchange-correlation term derived from the homogeneous electron gas but its utility in multi-atomic systems, where the charge density varies rapidly, is well proven. The exchange energy in H F theory is a four-center integral and its

328

R. C. NEWMAN AND R. JONES

evaluation requires the computation of O(N4)integrals, where N is the basis size. This is to be contrasted with LDF theory where the exchangecorrelation energy is an integral of a function of the electron density n ( r ) and its evaluation requires O ( N * M )computations where M is the number of points or operations involved in estimating this integral. The development of pseudopotentials (Yin and Cohen, 1982; Bachelet, Hamann and Schluter, 1982) that remove core electrons from the problem, leaving only the valance electrons to be considered, has been essential in allowing systems containing large numbers of Si atoms surrounding oxygen to be treated. The total electron density is composed of two parts, namely, a core density, which is the sum of contributions from different atomic cores and is large near each nucleus but falls off rapidly to zero outside the core, and the valence charge density, which although varying rapidly near the core (because of the constraints imposed by orthogonalization) is relatively smooth round the centers of chemical bonds. Norm-conserving pseudopotentials (Bachelet et al., 1982) have pseudowavefunctions that agree exactly with those of the true atom outside the core. Thus the charge density, exchange-correlation potential and Hartree potential derived from the pseudopotential are exactly the same as those given by a full atom calculation. Inside the core, the pseudopotential has a repulsive part making the pseudo-wavefunctions smooth and nodeless and this makes it easier to represent them with a simple basis-although the 2p 0 orbital causes problems when a basis of plane waves is utilized. This repulsive potential is chosen so that (a) the energy levels agree with the valence levels of the atom, (b) the scattering phase shifts are the same for the atom and pseudo-atom and (c) the core of the pseudo-atom contains the same charge as the true atom. These properties make the repulsive potential dependent on the orbital angular momentum and consequently the pseudopotential is a nonlocal operator. The belief is that these pseudopotentials can correctly describe different types of bonding between atoms but there is no formal proof of this. The nature of the exchange energy in HF theory involving the product of four orbital functions, some of which may be core ones, has made it more difficult to develop reliable pseudopotentials. It is for this reason that few calculations on large systems have been carried out (but see Mark et al., 1989; Nada et al., 1990) and instead a multitude of approximate methods have been developed. Those with the abbreviations CNDO and M I N D 0 ignore integrals representing matrix elements involving a pair of basis functions at distinct sites. Of course, there is no compelling mathematical reason for this, and it is then necessary to adjust the diagonal contributions. This is done by using fits to an empirical data base consisting usually of equilibrium geometries, ionization potentials and

8.

DIFFU5ION O F OXYGEN IN SILICON

329

other spectroscopic information. It is difficult to be persuaded that these methods can consistently model oxygen defects correctly, especially those far away from the fitted data base at a saddle point or other unusual bonding configurations. Nevertheless, there has been an accumulation of wisdom in using these methods extending over a decade, and the method, in the right hands. can yield great insight into complex defects and processes. It appears, for example, that the geometries predicted by the method are often very good; the frequencies of local vibrational modes are invariably overestimated, but often by a constant amount that allows systematic scaling. Deak and Snyder (1987) employ a variant of the M I N D 0 / 3 scheme, namely, ;t cyclic-cluster scheme, in which the wavefunction is forced to be periodic within the cluster. The method seems to give surprisingly good formation and migration energies. Nowadays, however, the emphasis is on using ab initio or more correctly parameter-free methods. There is no appeal to any empirical data base but the main deficiencies lie in The simplistic treatment of exchange-correlation; B . The incompleteness of the basis sets used to represent the wavefunction or charge density; c. The size of the cluster or supercell; D. The difficulty in assessing whether the relaxation procedure has produced a global or local energy minimum (i.e., one corresponding to a metastable structure); E. The convergence of the difference in the energy of the stable and saddle-po'int structures for the determination of migration energies; F. The accurate location of donor and acceptor levels that control the charge states of the diffusing species; G . The limitation to zero-temperature that prevents thermal expansion effects from being included.

A.

In practice, it seems that the methods can yield excellent structures and fair vibraticinal modes, but the errors in defect energies are much greater. For example. the oxygen molecule has been studied by spinpolarized LDF 1:heory (Kutrler and Painter, 1992). The O2 bond length was found to be I .21 A compared with an experimental value of 1.207 A . The frequen'cy of the stretch mode is calculated to be 1606 c m - ' compared with ;in observed one of I580 c m - ' , but the binding energy. 7.53 eV, is 44'3greater than that observed (5.21 eV). This can be substantially improved lo 5.4 eV if gradient contributions to the exchange correlation energy are used. Up to now, these have not been used to treat oxygen diffusion. It is uxually considered, however, that much of the

330

R. C . NEWMAN AND R. JONES

error in the binding energy occurs for the dissociated structure and that energy differences between similar structures are given more accurately. For H F itself, the method of PRDDO (partial retention of diatomic overlap) developed by Halgren and Lipscomb (1973) has given useful results in a number of problems involving impurities in Si-especially hydrogen and oxygen (Estreicher, 1992). Here one is judicious in the neglect of products of basis functions by requiring the basis functions to be orthogonal. Only the four center integrals involving distinct sites are neglected. In this way no parameters are necessary and the method seems efficient at giving sensible bond lengths. There are difficulties for saddle point energies-invariably too large (an effect that can happen in any theory where a seriously incomplete basis is used) and in determining vibrational modes. Gaussian basis functions have been a popular choice for both CNDO and MINDO, as well as LDF theories. Saito and Oshiyama (1988) as well as Jones ( 1988) describe methods of implementing LDF schemes, using such orbitals, for clusters. In the cluster method it is necessary to terminate the cluster in such a way that the properties of the inner part are insensitive to this surface. Most workers have used H atom saturation. The idea here is to passivate surface dangling bonds that would otherwise draw charge from the inner part of the cluster to the surface and interfere greatly with the properties of the defect lying there. It is important to choose a short H-surface length as this depresses the H-bonding states below the bulk valence band top and elevates the H-antibonding states to energies above the bulk conduction band. However, since the host feels a confining potential from the surface H atoms, its valence and conduction bands are also depressed and elevated, respectively, resulting in an increased band gap. However, it seems that this band gap widening does not significantly affect structural or vibrational properties, although it does lead to defect levels lying deeper in the gap than observed. It is known that small Hterminated molecules have structures and vibratory modes close to those of the bulk. For example, disiloxane, (SiH,), 0, has an 5-0 length of 1.634 A and vibrational modes at 1107 cm-' and 606 cm-I, which lie close to those parameters for interstitial oxygen in Si, namely, 1.6 A, 1136 cm-l and 515 cm-' (Stavola, 1984). Saito and Oshiyama (1988) use clusters containing up to 36 atoms, whereas Jones, Oberg and Umerski (1991) as well as Estreicher (1990) use clusters up to 86 atoms. There are two ways of avoiding the use of clusters. One uses either a Green function technique or a supercell. Kelly and Car (1992) describe a Green function approach using Gaussian orbitals and incorporating pseudopotentials. The advantage of this method is that one treats an isolated

8.

DIFFCI5ION O F O X \ G E N IN SILICON

33 1

defect in an infinite Si lattice. The usual problem with the Green function method is the difficulty of including the relaxation of a large number of atoms. The more atoms one relaxes. the greater the number of elements of the Green function that are required and this makes the method very time consuming. Other LDF calculations have been carried out using plane waves and a supercell sometimes with the molecular dynamical method of Car and Parrinello (1984). Here one treats the degrees of freedom of the electrons, namely, the coefficients of the expansion of each orbital in terms of plane waves, together with the positions of the ions as a set of generalized coordinates in analytical dynamics. The Lagrangian for this system can then be written down together with the equations of motion. These can be solved as in the usual molecular dynamical method. The ion temperature is then gradually reduced to enable the system to assume the lowest potential energy. This technique allows very large numbers of plane waves to be used in the basis. Needels et al. (1991) adopt it to relax unit cells containing up to 65 atoms with the Kleinman and Bylander (1982) form of the pseudopotential.

2.

T H E O R Y OF T H E

DIFFUSION cONSIAN'I

The standard amlytical tool for an evaluation of the hopping rate. for, say, 0;from one bond center to the adjacent one, is provided by reactionrate theory (Vinyard, 1957). Here the adiabatic potential energy surface plays a fundamental role. Thc Born-Oppenheimer approximation is used at the outset to describe the cnergy of any assemblage of atoms in terms of their positions only, the electrons being assumed always to occupy the ground state, The theory assumes that this potential surface, in the neighborhoods of both the stable and saddle points of the diffusing species, can be approximated by a Taylor series expansion up to secondorder terms. Of course the first-order terms are absent as the energy derivatives vanish at the stable and saddle points. The second derivatives of the energy at these points determine, via the dynamical matrix. the vibrational frequencies of atoms. At the saddle point, at least one of these frequencies is imaginary as the energy is locally a maximum along the corresponding normal mode. We suppose that the real frequencies at the stable and saddle points are i',and w,'. respectively. It is further assumed that, as a result of thermal fluctuations. the system visits each of these points as time evolves but if it enters the saddle surface then it always crosses it so that a diffusion event occurs. The ergodic assumption of statistical mechanics tells us that the relative probability of the system being in each of these points is related to the free energy of each. The

332

R . C. NEWMAN AND R . JONES

jump rate from the stable to the saddle point is then given by (Vinyard, 1957) rIVi

-exp( - AE/kBT). IIV,!

Here AE is the adiabatic potential energy difference between the saddle point and the stable one. Strictly speaking, this energy should include the effects of thermal expansion. If we identify the pre-exponential factor as a Debye frequency scaled by motion entropy, this rate is written as v exp(ASlk,

-

AE/k,T).

(7)

Now, the pre-exponential factor observed for the diffusion constant is 0.13 cm2 s - ' (Table 11) (Mikkelsen, 1986) and leads to a jump attempt rate of 3.5 x I O l 4 s - ' , which is about 35 times the Debye frequency, suggesting a motional entropy of about 3-4kB. There are several ways in which this entropy can be greater than zero (Stoneham, 1989). A. A saddle-point structure could have one or more very low frequencies. We shall discuss this later and suggest that the saddle surface does appear to be quite flat; B. It could result from thermal expansion. Stoneham (1989) finds a large effect due to thermal expansion on the cation mobility in MgO and it is not unreasonable that a similar effect would occur for Oimigration in silicon. C. The occupied gap levels at the saddle point may be temperature dependent. The Si band gap decreases quite rapidly with temperature leading to an effective entropy of about 5 k B . If there were an occupied gap level in the saddle-point configuration that also became shallower with increasing temperature, then one would expect the effective activation energy, A E ( T), to be temperature dependent. This follows from the fact that this occupied energy level also contributes to the total energy. Writing AE(T)

=

AE(0) - akBT,

(8)

shows that the entropy includes the term a . None of these effects has been properly discussed in relation to oxygen diffusion.

3. INTERSTITIAL OXYGEN Interstitial oxygen, O i , is not found at any high symmetry site in the Si lattice but it is customary to refer to its location as the nearest such

8.

333

DIFFLI5ION O F O X Y G E N I N SILICON

FIG. 2 0 . Location of various high-symmetry 4tes in the diamond structure. T is the tetrahedral interstitial site. H is the hexagonal interstitial site, BC is the bond center. and C is at the center of a rhombus formed by three adjacent Si atoms and the nearest T \ite. The M site is midway between two c' sites; it is also located midway between BC and a neighboring H site (Van de Walle. 1991 1.

Calculat iori

Snyder. Wu and Deiik. 1989 Ebtreicher. 1990 Jones et al.. 1991 Saito and Oshiyarna. 1988 Kelly and Car. 1992 Needels et al.. 1991 Bowmworth el al.. 1970 Newman. 1973

SI-0 Length (A)

Modes.

Barrier'

Angle (deg.)

(ern-')

(SV)

I80

1275. 699

SI-0-SI

I61 I $66 I 5Y I 6x I 77 I h4

I64

I72

1104. 554

152

I I87

I40 140 162

1136. 518

2.5 3. I 2.X I. ? 2.5

I .x 25

~~~~~

'The barrier for a diffusion jump relet\ to the C site

site. Thus oxygen at a bond center (BC) site refers to 0; near the center of neighboring Si atoms. Other important sites are t h e center of next-tonearest neighboriing Si atoms (the C site), and the antibonding (AB) site found midway between a Si site and the nearest interstitial tetrahedral (T) site. There is general agreement that 0,is stable at a BC site (Fig. 20). Table 111 shows the properties of this defect as calculated by different groups. Most workers allow the 0, atom and perhaps two shells of host atoms to relax. Kelly and Car (1992) allow the 0, atom to move perpendicular to the Si-Si bond from its BC site. while this bond, together with its neigh-

334

R. C . NEWMAN AND R. JONES

bors, can expand along their lengths. Their calculated length of the Si-0 bond seems to be too large to explain the high-frequency asymmetric Si-0 stretch mode, as it is recalled that the observed Si-0 length in disiloxane is 1.634 A, yet the frequency is close to that of 0;. The general consensus is that the Si-0 bond length for 0; is around I .6 rather close to that found in a-quartz, 1.60-1.61 p\ (Levien, Prewitt and Weidner, 1980). There is greater variation in the Si-0,-Si angle. It seems quite difficult to calculate this as there appears to be a rather flat potential energy surface for greater Si-0 lengths and smaller angles. Bosomworth et al. (1970) estimated this angle by fitting overtones of the 29.3 c m - ' bend mode to a simple potential for which they deduced a Si-0,-Si angle to be 1 6 4 , supposing a Si-0 length of I .6 A. The symmetric and asymmetric stretch modes are well reproduced by most calculations. Jones et al. (1992) also found their isotopic shifts to be in good agreement with experiment. The energy barrier for a diffusion jump of Oihas been calculated by a number of groups, who often assume that the saddle point occurs near the C-site. Jones et al. (1991) explicitly verified this assumption by mapping out the potential energy surface obtained by their LDF cluster approach. Saito and Oshiyama (1988) also showed that the C-site is unstable. The saddle-point structure is relevant to understanding how the barrier can be reduced by the presence of other defects. Jones et al. (1991) find the Si( 1)-0, Si(2)-0 and Si( I)-Si(2) bonds (see Fig. 21) have lengths 1.54, 2.31 and 2.86 (broken) A, respectively, together with an occupied low gap level. Saito and Oshiyama (1988) give 1.74, 1.9 and 2.62 A for these lengths with mid-gap occupied and empty levels. Snyder and Corbett (1986) give 1.67, 2.02 A for the first two 0-Si lengths, whereas Kelly and Car report 2.0, 1.93 A and Needels et al. (1991) find

A,

FIG.21. Oxygen at the C-site

8.

DIFFUSION ( I F O X Y G F N IN SILICON

335

1.69 and 1.93 A . Kelly and Car find only an acceptor state low in the gap. Thus there are very great differences between the calculations. This may be because the potential energy near the saddle point is rather flat, and this in turn might lead to low vibration frequencies there explaining the large entropy factor mentioned previously. Turning to the diffusion jump energies given in Table 111, we note the wide disparity of values. Snyder. Wu and Deak (1989) and Jones et al. ( 1991) report barriers close to that measured (2.5 eV). Estreicher's barrier is too large but this is not unexpected, as the barriers are sensitive to the sizes of basis sets. Other barriers straddle t h e measured value, and the differences are usually regarded as reflecting the technical deficiencies of the calculation, e.g., the inadequate size of the cluster, basis or relaxation method used. A counterview is taken by Ncedels et al. (1991) who believe that the adiabatic saddle point is indeed 0.7 eV lower in energy than the measured value of 2.53. This deficiency would then imply the breakdown of reaction rate theory. They argue that although an 0; atom, provided with about 1.8 eV of kinetic energy moves close t o the saddle point, it fails to open up the attacked Si-Si bond and returns to its starting point. They suggest that the 0, atom must develop kinetic energy of around 2 . 3 eV to avoid this return. However. it is not clear that the 0 atom will invariably return to its starting point and especially so if the attacked Si-Si bond is provided with at least a share of the 1.8 eV, allowing it to open up and permitting the energetic 0 atom to enter its bond center. The deficiency of 0.7 eV found by these authors might arise from the method employed. the pseudopotential used or indeed the use of LDF theory. This is a serious charge against the theory and further work is called for. 4. DIFFUSION OF 0, CA.I.ALYZEU HL HYDROGEN

There are two theories for the enhancement in the diffusion jump rate of 0, in the presence of H. We emphasiLed previously that in the saddlepoint structure one of the silicon atoms, Si(l) of Fig. 21, possesses a dangling bond. A nearby H atom may form a strong bond with this Si atom. leading to a reduction in the saddle-point energy. This assumes that, in the starting structure, when 0 is at BC site, the hydrogen is only weakly bound. Estreicher (19990) found that a H atom in the starting structure was most stable at a BC site adjacent to 0,.The energy for a metastable state with H near one of the three equivalent T sites (Fig. 2 2 ) was 0.66 e V higher. He argued that. when H is located near this metastable T site, it is able to lower the barrier for 0 migrating to the C site through the

336

R. C. NEWMAN AND R. JONES

FIG.22. The configurations of atoms according to Estreicher (1990) for 0, diffusion in the presence of hydrogen: (a) BC sited H , (b) H at T site, (c) saddle point, involving 0, with normal coordination and H overcoordinated, (d) final state with same energy as (a).

formation of the Si( 1)-H bond and leaving 0 bonded to two atoms. This barrier, when H is initially at the T site (Fig. 22), is 1.25 eV and is much lower than that in the absence of H. The final configuration then consists of H and 0 at adjacent BC sites. It seems to us, however, that the true activation energy must include the energy necessary for the H atom to get to the T site from the lowest energy configuration, i.e., a BC one, provided that thermal equilibrium prevails. This simply adds 0.66 eV to the preceding barrier and still provides a significant reduction of the 4.1 eV barrier found in the absence of H (Table 111). However, Estreicher argued that thermal equilibrium is not established and that an H atom is unable to enter the BC site, in the absence of O i , because of a high barrier between it and the T site. Thus, when H is introduced into the crystal, it diffuses by jumping between T sites and rarely enters a BC site; if it did enter a BC site it would remain trapped there. The diffusing Oiatom, however, promotes a movement of H into the BC site. He argued that a muon spin rotation experiment in oxygen-rich Si provides support for this viewpoint as no signal is observed due to muons located at T sites, in contrast to 0-free Si (Patterson

8.

DIFFU5ION (Ib OXYGEN IN SILICON

337

et al.. 1984). This view, that H is unable to reach its lowest energy site is not universally shared, as other calculations show rather low barriers for H to transfer from BC and to T sites (van de Walle et al., 1989; Buda et al., 1989; Briddon and Jones 1990). The energy profile during the migration is sketched in Fig. 2 3 . There is a problem with this model concerning what happens during subsequent oxygen jumps because i t is not clear whether the 0 - H complex dissociates or whether another H atom promotes the later 0,jumps. Jones et al. (1991). however, did not find the BC site adjacent to 0, to have the lowest energy for H but instead t h e AB site opposite Si-0-Si (Fig. 34). They believed the stability of this site was caused by polarization of the H atom originating from the Si-0-Si unit. The Si-H length was 1.5 A. and there was ;I hydrogen-related singly occupied mid-gap level. Relative to this structure. the energy of the BC site was higher by 1.5 eV and there were increases of 0.75 eV at the other three T sites. With H at the AB site and with 0 moved to the C-site, the energy increase is only 0.2 eV. Thus the previous barrier of 2.8 eV (Table 111) has been effectively eliminated. This is because the Si(I)-H bond has strengthened and reduced in length to 1.45 A. A H-related gap level is now filled and lies close to the valence band, E, . There remains a partially filled mid-gap state that is localized on 0 and has some overlap with the H atom. Now, when 0 moves away from the C-site, the energy increases because the Si(l)-H bond starts to weaken and a bond is formed between Si(I) and Si(2). The new activation barrier is found to be 1.4 eV, somewhat lower than the observed barrier. When the 0 atom moves to its

(a)

(b)

(c)

(d)

FIG.2 3 . Energy profile during 0, migration. according to Estreicher (1990):(a). ( h l . ( c ) . and ( d ) refer to the sites 5hown in Fig. 22.

338

R. C . NEWMAN A N D R. JONES

(c)b

Si

Si #'

0''

FIG.24. Configuration of atoms during 0,migration in the presence of hydrogen according to Jones et al. (1991): (a) H at AB site to Si-0,-Si, (b) saddle point with overcoordinated 0 only. ( c ) T site, (d) final structure with same energy as (a).

new bond-centered site, H is now no longer in the lowest energy configuration and must jump to a new antibonding site. It has to move to the further one if long range Oi migration is to occur. The energy profile is sketched in Fig. 25. It is not possible to say which of these two models is correct at the present time. Both of these theories assume that H is in a neutral charge state. Consider now the diffusion of Oiin the presence of H + or H - . Here, the starting structure possesses donor and acceptor H-related gap levels at, say, E d , and E,, , respectively. If the saddle point involves a strong Si-H bond, the H-related level must be full and low lying. There are likely to be higher gap levels, Ed2 and E,, associated with trivalent 0, which are empty and filled in p-type and n-type Si, respectively. The activation energy is then changed from the neutral case by (Edl-EdZ) in p-type Si and (E,,-E,,) in n-type Si. If Ed2 > E d , , and E,, > E,, in p-type Si, we would expect the rate of diffusion jumps to be further enhanced, but H - would inhibit the process. However, it is possible to think of other mechanisms not involving a strong Si-H bond at the saddle point. It may

8.

339

D I F F U S I O N ofi O X Y G L N I N SILICON

be that H' forms a direct bond with O,, weakening the two Si-0 bonds and hence promoting diffusion of 0 - H but this needs to be investigated. In either case, one expects that the catalytic effect of H upon 0 diffusion to be Fermi-level dependent. 5 . THEOXYGEN DIMER

The first stage of 0, precipitation is considered to be the formation of a dimer. It appears that a pair of nearest neighbor bonded interstitial oxygen atoms is a more stable arrangement than one involving the formation of an oxygen mo/rcu/r (Kelly. 1989; Snyder et al., 1988; Needels et al., 1991). This result is in conflict with the idea of Gosele and Tan (1982) that rapidly diffusing mo/e.c.u/rslead to enhanced oxygen diffusion. Derik, Snyder and Corbett ( 1992) reported that Si, generation is endothermic at least for aggregates of less than four 0, atoms. Thus, there is no theoretical support for the old idea. based on the volume of SiO,. that Si, must be generated during the initial stages of precipitation. The current view is that the dimer consists of a di-oxygen interstitial defect bonded to the Si lattice. Snyder et al. (1988) found that a buckled dimer (Fig. 26) was stable with a binding energy of 0. I eV. Jones (1990), Umerski and Jones (1992) and Kelly (1989) found that a pair of oxygen atoms placed at two adjacent bond-centered sites buckled outwards from each other, although Kelly reported a small binding energy. Needels et al. (1991) found a binding energy of I eV (for an unexpected geometry of the two 0 atoms lying above and below the plane of the two Si-Si bonds they break). The defect has no gap states. Umerski and Jones (1993) found

(a)

(b)

(c)

(d)

FIG 2 5 . Energy profile during 0, migration in the presence of H . according to Jones e t al. (1991): ( a ) . ( b ) . ( c ) and ( d ) refer 10 the bites \hewn i n Fig. 24.

340

R . C. NEWMAN A N D R . JONES

FIG.26. Buckled oxygen dimer structure (Snyder et al., 1988).

that the 0-Si-0 lengths are shortened to 1.53 A, whereas the other two 0-Si bonds are 1.6 This implies that there should be two asymmetric stretch modes with at least one lying above the 1136 c m - ' mode of 0,. N o experimental evidence for these modes has been reported from IR measurements. This may be understood if the defect was rather mobile forming a trimer. Indeed Snyder et and diffused quickly to another Oi, al. (1988) found an extremely low migration energy of the dimer of only 1.36 eV. They argued that the saddle point or its migration is close to a four-membered ring of two trivalent 0 atoms and a pair of Si atoms (Fig. 27). In essence, one 0 atom pulls the other through the barrier. Presumably the reason for the low migration barrier is that the saddle-point structure is stabilized, perhaps by a mechanism similar to that discussed earlier for the H atom. The essential point is that the silicon atoms are always fourfold coordinated and no Si dangling bond is created. Few details are given in the calculation and it would be useful to have this result confirmed by others.

A.

0 FIG.27. Saddle-point structure for oxygen dimer migration (Snyder et al.. 1988).

8.

DIFFUSION O F OXYGEN 1N SILICON

34 I

There has been considerable theoretical work on a vacancy containing a single 0 atom. The V 0 defect (A-center) (Watkins and Corbett, 1961: Corbett et al., 1961 1. and this has been discussed by DeLeo, Fowler and Watkins (1984). using MIND0 and X-a methods applied to H-terminated clusters containing up to 53 atoms. They found that 0 moved off-site along [IOO], as is observed, by about I A for a smaller 17 atom cluster and much less so for a largei- one. For the smaller cluster, t h e barrier to a reorientation of the oxygen atom within the VO defect is 0.47 eV. close to the measured value of 0.38 eV. Using a large cluster and modified spring constants for more remote atoms, they deduced the 0 stretch mode frequency to be 806 cm I. in excellent agreement with that of 836 cm (77 K ) observed experimentally but no attempt was made to calculate the migration barrier of the A-center. Snyder et al. (1989) and Deik et al. (1989) reported MIND013 calculations on 53 atom clusters and found that 0 moved off-site by I .22 A along a [ 1001 direction. The Si-0 bond lengths were I.66 A. and the 0 stretch mode occurred at 908 cm I . The upper region of the gap contained a bonding and antibonding pair of defect states, rather close together. N o information was given about the reorientation energy. Chadi ( 1990) reported that the Si-0 bond lengths, the weak Si-Si lengths and the Si-0-Si angle for the negatively charged defect were 1.7 A, 2.61 A and IW. respectively. Kelly (1989) found that the 0 atom lies along a [ I I I ] direction in contradiction to experiment. DeLeo. Milsted and Kralick ( 1985) and Snyder et al. (1989) have also investigated VO:. They both reported structures with Dld symmetry. in conflict with the observations of Bosomworth et al. (1970). However their calculated E vibrational modes at 847 c m - ' and 951 c m - ' . respectively, are in excellent agreement with that observed at 889 c m - ' . Snyder et al. (1989) calculated Si-0 lengths of 1.67 A and the 0-0 separation to be 2.66 A for this defect.

'

~

6 . Oxy-vgeti Conip1exc.s bt9ith S ~ . l f l l ~ ~ ~ . r - s t i t i a l s

Deak et a]. (1989. 1991, 1992) discussed O i l and ( 0 , ) : I complexes. They found that the 0 atoms readily formed over coordinated defects just as at the saddle-point structure (Fig. 21). If 0 forms a third bond, from the overlap of an 0 lone-pair orbital with an occupied sp3 Si hybrid. then an antibonding state must be occupied. The level associated with such a state must lie high up in the gap, and the defect would readily act as donor. They suggested that the defect shown in Fig. 28 is a candidate for

342

R . C . NEWMAN A N D R. JONES

tZ

Silicon atom

0 Oxygen atom FIG.28. 0,Ithermal donor model (Deak et al., 1992).

the thermal donor. There is support for oxygen over coordination from theoretical investigations of the Cj-Oj defect (Jones and Oberg, 1992) and from instabilities in simple models of thermal donors as mentioned earlier (Jones, 1990). In the former case, the 0 atom is bonded to a third Si atom, which is positively charged, having lost its electron to an adjacent carbon interstitial atom. This interaction stabilizes the overcoordination so that the defect thermally dissociates at a relatively high temperature of 300°C. Two important and unanswered questions concerning this model of the donor by Deak et al. are (a) whether its binding energy is sufficient to allow it to remain stable at 350-450°C and (b) what is the origin of the silicon interstitials that form the defect. It is essential to obtain accurate answers to these questions before the model can be accepted as a serious candidate for the thermal donor. VII. Constraints on Models of Thermal Donor Centers

Unless hydrogen impurities are present, the evidence for enhancements in Doxyin as-grown samples is minimal for 500°C 2 T 2 400°C: there may be an enhancement not exceeding a factor of -10 at 350°C during very extended heat treatments (Section 111.3) but a negligible enhancement at 450°C. These conclusions have important consequences relating to the maximum size of oxygen aggregates that can form at low temperatures, which in turn places severe constraints on models of TD centers. The set of coupled differential equations describing the aggregation of Oiatoms to form oxygen clusters O,, O,, etc. with the assumption of diffusion limited kinetics has been given by Tan et al. (1986) and related

8.

343

DIFFUSION Oi- 0 X Y G L . N IN SILICON

to measurements of the rate of loss of 0, atoms from solution during furnace annealings at 450°C. It was first assumed that there were no oxygen clusters present in the as-received material and calculations then led to the evolution of the various aggregates as shown in Fig. 29. A normal value of Do,y was required to explain the rate of oxygen loss, leading to the conclusion that loz] IO" cm-' and [O,] - 1Olh c m - ' after some 100-300 hrs of annealing. An important point is that [O,] is much greater than the concentration of [TD] 10l6cm13, while [TD] is much greater than LO,]. It follows that if TD centers involve only O2 defects in their cores, not all O2 defects can be TD centers. On the other hand, the possibility that TD centers contain 0, cores would be excluded on the basis of this model. However. if 0, defects were significantly more mobile than 0,atoms (Gosele and Tan. 1982; Gosele et al., 1989) it would be possible for them to be trapped by remaining 0, impurities to form 0, centers at a rate effectively equal to the previous rate of formation of O2 defects. It follows that the rate of loss of 0, from solution would be greater than originally calculated by -SO%, but this change could be accommodated by reducing the estimated value of Do,, (or the capture radius, r, , Section 111.3) by 33%. The resulting O3 defects would then be converted to 0, defects in a concentration of -10" cm-3 after -200 hrs by the capture of another diffusing 0,atom. However, it would be difficult to identify an 0, defect with a thermal donor, as the formation rate of

-

-

0

1

2 3 4 Anneal time ( 1 Oz h)

5

FIL. 79. The evolution of oxygen aggregates 0:.01,04.etc.. with annealing time at 450°C' calculated for a normal value of I),,,, (Tan el al., 1986).

344

R . C . NEWMAN AND R. JONES

the latter defect has now been shown to be proportional to [0,12 at T < 400°C (Londos et al., 1993). In their second model Tan et al. (1986) assumed that there were grownin O2 centers in a concentration of 9 x loi6 cm-3 in their as-received silicon bodes. The existence of a low concentration of such pairs is to be expected since there would be diffusion and aggregation of 0, atoms as the growing Cz crystal cooled to room temperature (Fraundorf et al., 1985). Measurements of the strength of the 9 pm band in heated samples sometimes show an increase compared with the strength in the asreceived material, implying that the heat treatment leads to the redissolution of very tiny oxygen aggregates (see, for example, Hahn, Shatas and Stein, 1986). Tan et al. (1986) went on to show that this second model could also explain their measurements of d[O,]ldr at 450°C. The calculated concentration of 0, centers remained close to 10'' cm-3 throughout the heat treatment, while the concentration of 0, clusters increased progressively and accounted primarily for the loss of 0,atoms from solution with a normal value of Doxy.It was again found that the calculated values of Doxyincreased linearly with [O,],. The possibility that 0, complexes might be identified with TD centers appeared to be less favorable than for the first model. The possibility that 0, defects were mobile was not considered, but if they were, there would be formation of larger oxygen clusters. There have been various measurements of the ratio of the loss of oxygen from solution to the number of donors generated A[O,]/A[TD]. Some of the reported variations relate to changes (28%) that have been made to the IR calibration coefficient of the 9 pm IR band (see Baghdadi et al., 1989), which in turn lead to changes in the estimated value of A[O,]. Other variations can be attributed to the presence of residual carbon impurities in samples, leading to values of A[O,]/A[TD] that are larger than for more pure samples. Taking an average for all samples, including those examined most recently (see Fig. 8 and Binns, 1994) the numerical value of the ratio is close to 10 ? 2 (using the calibration of Baghdadi et al.) for samples heated at any temperature T I450"C, irrespective of whether Doxywas normal or enhanced by the presence of hydrogen. The ratio was also constant for all heating times from zero up to the stage where [TD] became close to its maximum value. This result again demonstrates that not all 0, defects can be TD centers, but it is difficult to understand how TD centers could be associated with aggregates of oxygen atoms with no involvement of other components even if 0, pairs had a high diffusion coefficient. Thus, the formation of TD(N) from the similar double donor TD(N - 1) would require the incorporation of additional oxygen atoms, without increasing the number of donors, contrary to the

8.

DIFEU$ION O b O X Y L F N IN SILICON

345

almost constant value of AIOi]/AITD]. A possible defect is an /-atom, generated at some stage during the oxygen precipitation (see Mathiot, 1987, 1988). VIII. Summary

Microscopic measurements of Do,, derived from measurements of internal friction and the relaxation of stress-induced dichroism show that normal oxygen diffusion occurs by a single process over the whole temperature range from 1400°C to 300°C, with an activation energy close to 2 . S eV (Table 11). This result is in accord with first principles theory relating to diffusion jumps from one bond-centered site to the next. without the involvement of a vacancy. self-interstitial or a n y other impurity. These results have been supported by measurements of oxygen diffused profiles at high temperatures, and it has also been shown that the rate of oxygen precipitation is controlled primarily by the rate of diffusion. even though there is generation of self-interstitials at the matrix-precipitate interface. However, similar generation of /-atoms at the surface may lead to enhanced out-diffusion of 0, atoms at 750°C in carbon doped silicon. Further measurements are required to confirm this process. It is at lower temperatures (7' < 650°C) that there have been claims of enhanced oxygen diffusion which have gained wide recognition. One suggestion of an enhancement by a factor of lo4 to explain t h e formation of the structure originally believed to be coesite has been withdrawn, and the structure has been reassigned to hexagonal Si nucleated by I-atoms released during aggregation of 0, atoms. Subsequently, the reassignment has been questioned but no positive alternative interpretation was ad. vanced. Published SIMS measurements have implied values of D o x yenhanced by factors of up to lo4. and have been interpreted in terms of the rapid diffusion of Oz pairs. For 7 < 500"C, the evidence for enhancements in Doh!from direct measurement is in no sense overwhelming, unless samples contain hydrogen impurities or are subjected to 2 MeV electron irradiation. The latter process when there is sequential trapping of vacancies and 1-atoms by 0, impurities is easily understood, while two models have been proposed for interactions of hydrogen with 0, atoms and provide a basis for underInteractions of 0; impurities standing observed enhancements in with either vacancies or /-atoms alone have been examined by theory. and there is also experimental evidence that demonstrates the existence of binding energies with both types of defect. A central problem is to know whether or not there is a constant supply of vacancies or I-atoms present in heated samples. Contrary to an earlier suggestion. there is now

-

346

R. C. NEWMAN AND R. JONES

no evidence that the presence of metallic contaminants leads directly to enhanced 0;diffusion, but they may be lead to dissociation of H, pairs to generate atomic hydrogen so that Doxyis enhanced indirectly. We are then led to the following basic questions that still need to be answered. A. Do stable 0, defects form? These defects have not been observed by IR spectroscopy but they play the predominant role in proposed models of low temperature oxygen aggregation. B . If stable 0, centers form by two 0;atoms diffusing together, what is the magnitude of the capture radius? This result is important to the understanding of possible links between long-range diffusion and single diffusion jumps. In previous studies, Davies et al. (1987) have reported experimentally determined ratios of capture radii for various defect reactions involving V and I-atoms with numerical values up to 10.0 s 5.0. Since a minimum value of r, is 2 A, it is implied that larger values of rc = 20 k 10 A can sometimes occur. We have implied that a value of r,. = 10 A is appropriate to dimer formation but better fits of our data can be obtained with r, = 15 A. It would appear that these values cannot be dismissed as being physically unreasonable without further investigation. C. Are 0, defects more mobile than single Oiatoms? The answer to this question is of paramount importance with respect to the type of oxygen clusters that may form and to possible assignments to TD defects. In Section 111.2, we quoted the conclusions of Messoloras et al. (1987) that the measured rates of loss of oxygen from solution as a result of annealing in the range 500°C 5 T I600°C cannot sensibly be described by the theory of Ham (1958). In fact, the fitting of the data to theory yields two parameters, namely, c, and a rate constant K . The latter parameter is proportional to N"' Doxyand consequently, if the effective value of Doxywere enhanced by a factor of lo4, as shown in Fig. 4 (Gosele et al., 1989), the number density of oxygen aggregates would be lowered by a factor of lo6. In that case, the theory would be physically meaningful, because each particle would be predicted to contain -lo6 oxygen atoms after long anneals at SOOT, and it might be possible to identify the ribbonlike defects with oxygen aggregates (Bergholz et al. 1985). A clarification of the TEM data is required as a consequence of the work of Pirouz et al. (1990). D. Is there continuous generation of I-atoms during 0;atom aggregation at low temperatures when 0, formation would appear to be the dominant process for the loss of oxygen from solution? Evi-

8.

DIFFU\ION O F OXYGEN I N SILICON

347

dence relating to the loss of carbon from solution has been cited in favor of the process. but it is difficult to reconcile this proposal with first principles calculations for the formation of the I-atoms (Deak et al., 1992). If /-atoms are generated, they may be a major constituent of TD centers. If rapid diffusion of O2 occurs, so that there is formation of 0, aggregates, it could alternatively be proposed that there is f-atom emission at that stage. Further studies of TD centers by the ENDOR technique are required to distinguish oxygenlf-atom clubters from pure oxygen clusters.

In conclusion, it is now apparent that heat treatments of Si in hydrogen with E, = 1.7-2.0 eV that make ambients lead to enhancements in themselves apparent for 7 5 500°C. As a result, all the processes that depend on Doxq as the rate-limiting process are also enhanced by the same factor, including the formation of TD centers. The principal outstanding questions appear to be related to the properties of O2 defects. Further understanding will be difficult until answers are forthcoming to the questions that have been listed.

A(

KNOWLEDGMENTS

The authors would like to thank M . J . Binns, A . K. Brown. C. A . Londos. S. A . McQuaid. and J . H . Tucker for allowing their re\ult\ to he published prior to puhlication and a l w for their comment5 on the manuscript. C'. F.'. Dale I\ thanked for the preparation for the manuscript and N Powell for preparing the illu\ti-ations. The Science and Engineering Research Council of The United Kingdom are thanked for their financial support of this work

Abou-el-Forouh. F. '4.. and Newman. K . C . (1974). Solid Stcrtr Comrnrrn. 15, 1409. Bachelet. G. B . , Haniann. D. R.,and Schluter. M . (1982). P h y s . Re\.. E 26, 4199. Baghdadi. A , . Bulles. W. M . . Croarhin. M . C.. Li. Yue-Zhen. Scace. K . I . . Series. K. W.. Stallhofer. P . . and Watanahe. M (I'W.9). J . Elccfroc~lirmSoc~.136, 2015. Bemski. G . (1959).J . A p p l . Phvs. 30, I 195. Bergholr, W.. Hutchison. J . L . . and Piroul, P. 11985). J . Appl. Phy.,. 58, 3419. Bergholr. W.. Hinns, M. J . . Booker. G K . . Hutchison, J . C . . Kinder. S. H . . Messoloras. S . . Newman. R . C., Stewart. K . I . . and Wilkes. J. G. (1989). Phil. Mrrg. 59. 499. Binns. M . J . (1994). Ph.D. thesis, Clniver\ity of London. Bond. W . L.. and Kaiser. W . (1960). J . Phv.5. Clirrn Solids 30, 14Y3. Bosomworth. D. R . . Haye.;, W.. Spray. A . R L... and Watkins. G. D. (1970). Proc.. R o y . S o c . A 317, 133. Bourret. A . ( 1986). Mtrr. R e v . .So( . . S v m p . Pro(, 59, 223. Bourret. A . (19x7). !ti,\/. Plrv.\. ( ' o r i f . S t v 87, 39.

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R. C. NEWMAN AND R . JONES

Bourret. A.. Thisbault-Desseaux. J . , and Seidman, D. N. (1984). J . Appl. Pliys. 55, 825. Brelot. A. (1972). Ph.D. thesis, University of Paris. Brelot. A. (1973). In Radiation Damage and Defects in Semiconductors. J. E. Whitehouse (ed.), p. 191. Inst. Phys. Conf. Ser. 16. Brelot, A., and Charlemagne, J . (1971). In Radiation Efiects in Semiconductors, J. W. Corbett and G. D. Watkins (eds.), p. 161. Gordon and Breach, London. Briddon. P. R . , and Jones, R. (1990). Hyperfine Inferactions 64, 593. Brown, A. R. (1991). Ph.D. thesis, University of London. Brown. A. R., Claybourn, M., Murray, R., Nadhra, P. S., Newman, R . C.. and Tucker, J . H. (1988). Semicond. Sci. and Technol. 3, 591. Brown, A. R . , Murray, R . , Newman. R. C.. and Tucker, J . H. (199Oa). Muter. Res. Soc. Symp. Proc. 163, 555. Brown, A. R . , Tucker, J. H., Newman. R . C., and McQuaid, S. A. (1990b). In 2Uth Int. Cog/: on the Physics of Semicwnductors, E. M. Anastassakis and J . J. Jodnopoulos (eds.). Vol. 1, p. 553. World Scientific, Singapore. Buda, F.. Chiarotti, G. L., Car, R., and Parinello, M. (1989). Phys. Rev. Lett. 63, 294. Bullough. R.. and Newman, R. C. (1970). Rep. Prog. in Phys. 33, 101. Car. R . , and Parrinello, M. (1984). Phys. Rev. Lett. 55, 2471. Chadi. D. J . (1990). Phys. Rev. B 41, 10595. Chevallier. J., Clerjaud, B., Davies, E., Dumas, J.-M., Johnson, N., Newman, R. C., Stavola, M., Viktrovitch, P., and Zavada, 3. (1991). Ann. Tde'cornmun. 46, 171. Claybourn. M., and Newman, R . C. (1987). Appl. Phys. Lett. 51, 2197. Corbett, J . W., McDonald, R. C., and Watkins, G. D. (1964a). J . Phys. Chem. Solids 25, 873. Corbett, J . W., and Watkins, G. D. (1961). Phys. Rev. Lett. 7, 314. Corbett, J . W., Watkins, G. D.. Chrenko, R. M., and McDonald, R. S . (1961). Phys. Rev. 121, 101s.

Corbett. J . W., Watkins, G. D., and McDonald, R. S. (1964b). Phys. Rev. 135, A1381. Davies, G., Lightowlers, E. C., Newman, R. C., and Oates, A. S . (1987). Semicond. Sci. and Technol. 2, 524. Davies. G., and Newman, R. C. (1994). In Handbook on Semiconductors, Vol. 3, 2nd ed., S . Mahajan (ed.), North-Holland, Amsterdam, in press. Davies. G.. Oates, A. S . , Newman, R. C., Wooley. R., Lightowlers, E. C., Binns, M. J . . and Wilkes, J. G . (1986). J . Phys. C : Solid St. Phys. 19, 841. Dehk, P.. and Snyder, L. C . (1987). Phys. Rev. B 36, 9619. Deak, P., Snyder, L. C., and Corbett, 5. W. (1991). Phys. Rev. Lett. 55, 747. Deak, P.. Snyder, L . C., and Corbett, J . W. (1992). Phys. Rev. B 45, 11612. Deak, P.. Snyder, L. C., Corbett. J. W.. Wu, R. Z., and Solyom, A. (1989). Materials Sci. Forum 38-41, 281. DeLeo, G. D., Fowler, W. B., and Watkins, G . D. (1984). Phys. Rev. B 29, 3193. DeLeo. G. D., Milsted, C. S . , and Kralik, J. C. (1985). Phys. Rev. B 31, 3588. Estreichcr. S. K. (1990). Phys. Rev. B 41, 9886. Estreicher, S . K. (1992). Muter. Res. Synip. Proc. 240, 643. Fraundorf, G., Fraundorf, P., Craven, R . A., Frederick, R. A,, Moody, J . W., and Shaw, R . W. (1985). J . Electrochem. Soc. 132, 1701. Freeland. P. E. (1980). J . Electrochem. Soc. 127, 754. Fuller, C. S . , and Ditzenberger, N. B. (1956). J . Appl. Phys. 27, 544. Fuller. C. S., and Logan, R. A. (1957). J . Appl. Phys. 28, 1427. Gass, J.. Muller, H. H., Stussi, H . , and Schweitzer, S. (1980). J . Appl. Phys. 51, 2030. Gaworzewski, P., and Ritter, G. (1981). Phys. Stat Sokdi 67, 511. Gosele, U. (1986). Muter. Res. Soc. Symp. 59, 419.

8.

DIFFU\ION O F OXYGEN IN SILICON

34Y

Gosele. U.. Ahn. K.-Y.. Marioton. I3 P. K.. Tan, T . Y.. and Lee. S.-T. (1989).A p p l Plrvs. A 48,219. Gosele. U.. and Tan. T. Y. (1982). A p p l . Phys. A 28, 79. (iupta. S . . Messoloras. S . Schneider. J R.. Stewart. R. J . , and Zulehner, W. (1990). Srmic.orld. .Y(,i. trtrd 7Cc/lnol. 5, 7x3. Gupta. S.. Messoloras. S . . Schneidei-. J . K.. Stewart. R. J . . and Zulehner, W. (1991). J . A p p l . C I ~ S24. I . 576. Gupta. S . . Messoloraa, S . . Schneider. J K . , Stewart. R. J.. and Zulehner. W. (l992a). S f , W f i ( ~ ~ JSci. l I d . trnti 71,i hnol. 7. 6 . Gupta. S . . Meswloras. S . . Schneider. J R . . Stewart. R. J . , and Zulehner. W . (1992b). Serrlic~ond.Sci. ClMi TtTllnol. 7, 443. , C. (1960). J . P h y t . C / I ~ /S~/itl.\ ~ I . 15, 108. tiahn. S . (1986). M u r . Res. Sot.. S v n r p /’roc.. 59. 18. Hahn. S..Shatas. S . C.. and Stein. H . J . (1986). M o r r r . Res. So(.. S y m p . P r o ( . . 59, 287. Halgren. T. A.. and Lipscvmb. W N . 11973). J . Cllem. Phy.c. 58, 1569. Ham. F-. S . (1958). J . P/iy.\. C h c ~Solids 6, 335. k i n s e n . W. L . . Haller. E. E.. and Luke. P. N . (19x2). lEEE Truns. N14c.l.Sci. NS-29, 738. k i n s e n . W. L . , Pearton. S. J.. and Haller. E . E. (1984). A p p l . Phys. Ltw. 44, 889. Heck. I).. l’res5ler. R . E.. and Monkow5ki. J . (1983). J . A p p l . Phys. 54, 5739. H u . S . M .( I981 ). J . Appl. P/iy.\. 52. 7074 Ichimiva. I-..and Furuichi. A . i 19hX) / H I . J . Appl. Rud IsoroprJ 19, 2115. I h m . J . (1988). Repr. Pro,yress iir f j / r \ , . \ i ( .\ 21. 5735. Isoma. S..Aoki. S.. and Watanabe. K. (1984). J . A p p l . PhyA. 55, 8117. Itoh. Y.. and Nozaki, J . (1985).J a p . J . A p p l . P h ~ r 24, . 279. Jone5. R . (1988). J . P h y s . C: Solid .S/. Plrv.\. 21, 5735. Jones. R (1990). .Se~iic.ond.Scr. 7 ~ d r 1 r o l5,. 3 5 . Jones. K . . and Oberg, S . (1992). P/rv\. K r i . . L P I I .68, 86. Joneh. K.. Oberg. S . . and Umerski. A (1991). Mtr/ericrl Sci. Forum 83-87, 551. Joneh. K.. n , . called sfcible precipitates, growth is more probable than dissolution. while for n < n , (rrnstable precipitates) the opposite is true. The nucleation theory calculates the number of precipitates (nuclei) that grow per unit time from subcritical to supercritical precipitate sizes. The resulting (steady state) nucleation rate is given by (Hirth and Pound. 1963)

The dimensionless Zeldovich factor Z equals

For the frequency W of attachment of atoms to the nucleus

is set. with c0 denoting the surface condensation coefficient. D o the diffusivity of oxygen, (I the atomic .lump distance in the lattice and Co the

394

M. SCHREMS

concentration of interstitial oxygen. For spherical oxygen precipitates the critical radius r,. is related to the critical number of oxygen atoms by 4n -r: 3vo with v o being the precipitate volume per oxygen atom. n,.

=

b. Examples and Basic Results

Most of the oxygen precipitation models proposed until now are based on the VWBD theory, which is also called steady state nucleation theory. The models differ mainly in assumptions on the concentration of sites C , (Eq. (I)), the term used for the Gibbs energy of precipitate formation AG(n) and the value of the Zeldovich factor 2. In the homogenous nucleation models C, is set equal to the interstitial oxygen concentration (Freeland et al., 1977; Inoue, Wada and Osaka, 1981; Inoue, Wada and Osaka, 1987; Reiche and Nitzsche, 1985) by most authors. However, Voronkov et al. (1989) claim that by this assumption the mass action law is violated and suggest setting the concentration of nucleation sites C , equal to the total density of interstitial lattice sites in the crystal. Heterogenous nucleation models assume that C, is equal to the concentration of some other defect such as carbon (Kishino et al., 1982; Usami, Matsushita and Ogino, 1984; Isomae, 1991) or vacancy clusters (Ravi, 1974). The Gibbs energy AG(n = n,.) occurring in Eqs. (1) and (3) is frequently assumed to be equal to the sum of volume energy accounting for the formation of the precipitate from oxygen atoms in solid solution and interfacial energy of the precipitate due to interaction with the surrounding crystal atoms: AG(n,.)

=

-n,.k,Tln

i:;) + -

4nrf.a.

The interfacial energy parameter a (a = 0.43 J/rn2; Inoue et al., 1981)and the Zeldovich factor 2 are usually determined from matching calculated nucleation rates J (Eq. (I)) to values obtained from experimental results. For Z either a constant value (2 = 0.01; Inoue et al., 1981) or Eq. (3) (Reiche and Nitzsche, 1985) is used. Cbqdenotes the equilibrium concentration of oxygen in the crystal. The basic calculation result of the steady state nucleation models is the nucleation rate Eq. (2). The total precipitate density Copfollows from integrating the nucleation rate J with processing time Cop = J J d t

(7)

for a given thermal sequence. Examples of calculation results obtained by Inoue et al. (1981) can be seen from Figs. 1 and 2. A strong increase

10.

SIMU1.A I ION O F OXYGEN PRECIPITATION

395

Oxygen Content C, ( lOt7atoms/crn3) FIG. I. Nucleation rate at 750°C V.I initial oxygen concentration. Calculations were performed with a model based on steady htate nucleation theory. The expenmental oxygen concentration values in this figure were determined using a FTlR spectra conversion coefficient o f h ppma . cm. When compared to the other figures (DIN conversion coefficient of 4.9 ppma . em) the oxygen concentrations in thih figure have to he multiplied by 4.916. (After Inoue el al.. 1981. This figure wi15 originally presented at the Spring 1981 Meeting of the Electrocheinical Society held in Minneapoli\.)

of the nucleation rate with the initial oxygen concentration is observed both experimentally and in the calculated results for a processing temperature of 750°C. The nucleation rate as a function of temperature shows a peak for temperatures typically between 600°C and 800°C. It descends both for lower temperatures. which is determined by the lowering of the valuc of the oxygen diffusivity, and for higher temperatures, where the increase in the equilibrium concentration of oxygen is dominant. The values of the equilibriiim size-distribution function (Eq. ( I ) . Fig. 2 ) were found to decrease with increasing temperature (Inoue et al.. 1981). c. Applicability

Despite the good agreement between experimental and calculated precipitate densities found for a number of cases (Inoue et al., 1987; Reiche and Nitzsche, 1985; Voronkov et al., 1989; Babitskii et al., 1990), the steady-state nucleation models have substantial deficiencies in describing the oxygen precipitation process: 1.

The loss in interstitial oxygen due to oxygen precipitation and the average precipitate radius as a function of processing time cannot be calculated.

396

M. SCHREMS

\

104

lo6 104

loz

I1

loo LL 1

1

~~

2

1200 \ \llOO\’O‘ \ ‘, , 1 1 I 5 10 20 1

1

, ,u

\ I

50

100

Number of Oxygen Atoms in Embryo FIG.2. Equilibrium distribution functions of small precipitates (embryos) for various temperatures and an initial interstitial oxygen concentration of 1 1 . 10’’ cm-) (calibration as in Fig. 1) calculated with the same model as in Fig. 1. (After lnoue et al., 1981. This figure was originally presented at the Spring 1981 Meeting of the Electrochemical Society held in Minneapolis.)

The experimentally observed reduction in the total precipitate density for longer annealing times (e.g., Bergholz et al., 1989) cannot be described, since this would require negative values for the nucleation rate. From Eq. (2) it follows, however, that this cannot be achieved by the steady-state nucleation theory. 3 . The model is based on the assumption that the size-distribution function can be approximated by its equilibrium value.

2.

A transient nucleation theory containing the VWBD steady-state approach as a special case (Kashchiev, 1969; Toshev and Gutzow, 1972) may resolve problem (2), while problem (1) remains in any case.

2. DETERMINISTIC GROWTH MODELS u . Concept

All the models summarized by the term deterministic growth models share the assumptions that the precipitates can be regarded as equal in size and that their number is constant with processing time. The oxygen precipitation process is thus described only by the variation with time of a “deterministic” average precipitate size instead of using the more general

10.

SIMULATION OF OXYGEN PRECIPITATION

397

size-distribution function. which is based on the picture of statistical growth and dissolution processes for all precipitate sizes. With the additional assumption that the precipitate dimensions are small compared to the interprecipitate distance, direct diffusional interaction between precipitates can be neglected. The silicon crystal can then be divided into a number of cells each containing one oxygen precipitate with the net diffusional fluxes between individual cells canceling each other. An equation for the variation with time of the average precipitate size, which is also known as g r m l t h IuM’. is obtained by solving the diffusion equation for a single precipitate and its surrounding matrix area. Growth laws were reported for different precipitate shapes such as spherical (Wert and Zener. 1950; Ham, 1958). cylindrical discs (Flynn, 1964; Seidman and Balluffi, 1966; Hu, 1981; Wada and Inoue, 1985; Hu, 1986a, 1986b). oblate and prolate spheroids (Ham. 1958, 1959). Frequently models based on Ham’s theory of diffusion limited precipitation (Ham, 1958) are used. For spherical precipitates with an average radius f ( t ) as a function of time t an approximate solution of the transient diffusion equation yields the following growth law (Wert and Zener. 1950; Ham, 1958):

denote the oxygen concentration in the The symbols C,(t), C; and C,, bulk at the precipitate-matrix interface and in the precipitate. Considering the conservation of total oxygen an equation for evaluating the time dependent interstitial oxygen concentration C,(t) can be derived from Eq. (8) (Ham, 1958; Yatsutake, Umeno and Kawabe, 1984):

by assuming that the interfacial oxygen concentration is equal to the bulk equilibrium concentration C:;. C’,, denotes the total concentration of oxygen precipitates. The righthand side function H is given by

h. Esurnplrs uiid Basic Rrsults

Deterministic growth models were successfully compared with experimental data by a number of authors. For platelet-shaped precipitates (Wada, Inoue and Osaka, 1983) some experimental data for the increase

398

M. SCHREMS

1013

I

'

' """I

'

" " " q

800°C

~

0

.s Y

101'

a

.r

Ea 1010

1

10

100

1000

time [h]

FIG.3 . Precipitate densities vs. annealing time for two different temperatures. Calculations were made by using a deterministic growth model (solid lines). Experimental results (circles) were obtained from TEM investigations. (After Yatsutake et al., 1984.)

of precipitate size with annealing time could be explained by adjusting the value of the oxygen diffusivity until calculations meet the experimental data. Using Ham's theory for spherical precipitates, values for the oxygen diffusivity and the equilibrium concentration of oxygen were determined over a temperature range 500"C-l050"C (Livingston et al., 1984; Messoloras et al., 1987) based on experimental results for the loss of interstitial oxygen and the precipitate density after long-time thermal anneals. Earlier applications of Ham's theory calculated the total density of precipitates from given values of the oxygen diffusivity and the experimental data for the loss of interstitial oxygen (Newman et al., 1983; Binns et al., 1983; Wilkes, 1983). Yatsutake et al. (1984) determined values for the precipitate density from fitting experimental data for the loss of interstitial oxygen as a function of the annealing time by using a model based on Ham's theory for oblate spheroidal precipitates. The analytic equation used by Yatsutake et al. differs from Eq. (9) only by an additional lefthand side geometry-related factor, which approaches 1 when the oblate spheroid approaches spherical shape. The example in Fig. 3 shows that the calculated precipitate densities for two one-step anneals agree well with data from TEM observations. The average precipitate radii (Fig. 4) were determined from the conservation of total oxygen and are also well represented.

10.

SIMUI.ATION 01: OXYGEN PRECIPITATION

399

L

ec 10’

1

100

10 tinif,

1000

[ti]

FK, 4. Sire of platelet shaped oxygen precipitates vs. annealing time obtained from the w n e modeling and experimental study referenced in Fig. 3 . (After Yatsutake et al.. 19.84.)

c’.

Applicuhility

Contrary to the classical nucleation models discussed in Section 11. I . the deterministic growth models account both for growth and shrinkage of precipitates (see Eq. (8)). However, the concentration of precipitates Cop and the Loss of interstitial oxygen cannot be calculated simultaneously, since only one equation (e.g. Eq. (9)) is available. Furthermore, the concentration of precipitates is regarded as constant with annealing time. For a given annealing step with a fixed temperature. this may be valid after an initial transient period (Ham, 1958; Livingston et al.. 1984). For very long annealing times this assumption is also proven inadequate by experimental results (Livingston et al., 1984; Bergholz et al.. 1989) showing a reduction in the precipitate density with increasing processing time. which may be attributed to the growth of larger precipitates at the cost of smaller ones (“coarsening”). The assumption that all precipitates are equal in size may be considered a good approximation only if the precipitate size-distribution function is sharply peaked, which becomes more likely with longer annealing times and higher processing temperatures. In this context it is emphasised that precipitate size-distributions are not a pure theoretical concept, but that their existence is also observed experimentally (oxygen: Fraundorf and Shimura, 1985; antimony: Brabec et al., 1989; stacking faults: Patel, Jackson and Reiss, 1977). Therefore, a more detailed picture of the precipitation process can be

400

M. SCHREMS

given only by those models, which allow calculating the transient evolution of the oxygen size-distribution function. 3 . COMBINED NUCLEATION AND GROWTH MODELS a . Concept

The previous discussion has shown that nucleation models (Section 11.1) can calculate only the total concentration of precipitates during a

given annealing sequence, but not the total loss of interstitial oxygen or the average precipitate size. On the other hand, the loss of interstitial oxygen or the average precipitate size can be determined by using deterministic growth models (Section 11.2), if the value of the total precipitate density is known. Therefore, a combined use of the two model types seems desirable.

b . Examples and Basic Results Among the first published models suggesting a combined use of nucleation and growth models is the work by Usami et al. (1984). Oxygen precipitate nucleation (Eqs. ( 1 ) and (2)) was assumed to occur only at the site of a carbon atom. Oxygen precipitate growth was described by Eq. (8). Good agreement was reported between experimental and calculated oxygen reduction for a set of two-step annealing sequences using wafers with different carbon contents. Pagani and Huber (1987) proposed a model using homogenous nucleation by setting the concentration of sites in Eq. ( I ) equal to the interstitial oxygen concentration. Precipitate growth is described using Ham’s theory in the form of Eq. (9) from Section 11.2. For a multistep CMOS and a NMOS annealing sequence a correct prediction of trends in the experimental loss of interstitial oxygen as a function of initial oxygen was reported. Yang et al. (1987) formulated a model combining the use of nucleation theory and Ham’s theory with a one-dimensional diffusion equation. For several three-step HI-LO-HI annealing sequences the model could be applied to calculating the precipitated oxygen concentration and the density of precipitates in the bulk as well as in the near surface region of the wafer, where both precipitation and outdiffusion of oxygen contribute to the total loss of interstitial oxygen. Additionally, experimental and theoretical denuded zone depths were found to be in good agreement. Recently Isomae (1991) applied a model similar to the one proposed by Usami et al. (1984) for simulating oxygen precipitation both in three-step and in multistep CMOS-type annealing sequences. Experimental results could be satisfactorily explained only

10.

S I M U L A l I O N O F OXYGEN PRECIPITATION

1

40 1

10 100 Radius ( n m )

F I G 5 Size-distribution function X

0

0

5

10 I N I T I A L OXYGEN [1017cm-31

FIG. 10. Calculated (lines) and experimental (symbols, Schrems et al., 1990a) oxygen loss as a function of the initial oxygen concentration in a two-step thermal cycle for various growth times x at 1050°C. (Schrems et al., 1991c.)

tion region (Chiou, 1987; Swaroop et al., 1987). In the 100% region the interstitial oxygen concentration has reached the bulk equilibrium value. Any further increase in the initial oxygen concentration leads to a similar increase of the precipitated concentration. Consequently, this part of the S-curve becomes a straight line. The calculation results in Fig. 9 were obtained by adjusting the free parameters of a model using a FPE only (II.S.b.i, Schrems et al., 1989) to reproduce the experimental data available. In the calculations, however, the S-curve could then be easily completed for the whole regime of initial oxygen concentrations. After parameter extraction (Schrems et al., 1991a) simulations with the model based on CRE in combination with a FPE (II.S.b.ii, Schrems et al., 1991a, 1991b, 1991c, 1991d) yielded good predictions for data from FTIR measurements after one-step and two-step annealing as can be seen from Figs. 10 and 11. As shown in Fig. 12 experimental precipitate densities (curve for tcooling= 3 hr) could also be explained quite well. The characteristic time fcooling varied in the simulations shown in Fig. 12 accounts for the cooling phase during crystal growth and all other thermal pretreatments, which are known as thermal history. The thermal history of the wafers already results in a significant formation of small precipitates influencing succeeding anneals. For the case of a two-step LO-HI annealing, Fig. 12 shows an increasing influence of the thermal history on the calculated precipitate densities the shorter the duration of the LO anneal at 750°C. A typical distribution of interstitial oxygen after three-step HI-LO-HI

10.

SlMUL A [ I O N O F O X Y G E N PKECIPlTATlON

419

10

-

800°C/2h*10500C/16h 800"C/lh+1050"C/8h

n

E 0

>0 P I

Z W

9 X

0

0

5

a

7

4 INITIAL

9

10

OXYGEN [1017cm-31

F I G . I I . S-shaped curves showing oxygen l o s s vs. initial oxygen for a HI and three different LO-Hl annealings. Experimental results-symbols: Swaroop et al.. I987 (circles and r ) . Chiou, 1987 (stars: squares and diamonds represent averages over a larger number ofmeasurements). Schrems et al.. IWOa ( t )-are shown in order to check the calculations. (Schrems et al., l99lb.)

-

1013

h7

E V

I

~

1012

I

m

z

W

W

lo1' 10'0

w Ly

a

10-1

100

lo1

lo2

lo3

TIME t at 750°C [hl F I ( i . I ? . Calculated (lines) and experimental (lnoue et al.. 1981; circles) density of oxygen precipitate, as a function o f the 7 W ( ' nucleation-annealing in a two-step thermal process. for cooling during Thc \tar\ mark experimental error h i \ . I n the calculations the time r,l crv.;tal growth from 1400°C to 4CO'C' wah varied. (Schrems et al.. 1991c.)

420

M . SCHREMS

1100°C/16h+6500C/16h+ 1000°C/16h

1100"C/3h+650"C/l6h+ 0-

INTERSTITIAL OXYGEN PRECIPITATED OXYGEN

Y

Li

z

0

U

z W

5x

1

t 0

(a)

20

40 60 DEPTH [pml

80

0

100

0

20

40 60 DEPTH [pml

80

(b) FIG.13. Calculated interstitial (solid line) and precipitated oxygen concentrations (dotted line) as a function of depth from the wafer surface after two different three-step HI-LO-HI annealings (initial bulk oxygen concentration: 9.5 . 10'' cm-'). Circles mark the error bars for the experimental results reported by lsomae et al. (1984). The dotted lines show the calculated precipitated oxygen concentrations. (Schrems, 1993.)

annealings as a function of depth from the wafer surface is illustrated in Fig. 13(a), (b). In both cases the interstitial oxygen concentration declines from a peak value towards the surface and towards the inside of the wafer, where it reaches a constant bulk value. Due to the shorter HI anneals the peak value is less pronounced for the results in Fig. 13(a). The characteristic curve shape is due to the interaction of oxygen outdiffusion dominating in the surface near region left of the peak and an increasing loss of interstitial oxygen caused by increasing precipitation for larger depths, which finally approaches a constant bulk value. The denuded zone depths (Isomae et al., 1984; Yang et al., 1986; Schrems, 1993) may be estimated from profiles showing an increase of the precipitate density with the greater depths in the wafer. Alternatively analytical models for a direct calculation of DZ-depths were suggested (Wijaranakula and Matlock, 1991). The DZ depths were found to increase both with annealing temperature and the duration of the first HI annealing, but to decrease with increasing initial oxygen content in the wafer. When performing a detailed analysis of oxygen precipitation during a given thermal sequence computer modeling can be a very powerful method in providing additional data, which are not accessible to experimental investigations or only with difficulty. As an example bulk precipitation for the HI and LO-HI sequences from Fig. 9 was analyzed using

100

10.

SIMUI.ATION OF OXYGEN PRECIPITATION

42 1

the model based on a FPE only (Section 11.5.b.i, Schrems et al., 1989). For three representative points from the low ( A ) ,the partial ( B ) and the 100% precipitation region (C’)precipitated fractions. precipitate densities, average radii, size-distribution functions and critical precipitate radii were evaluated (Schrems et 31.. 1989). Some of the results are shown in Figh. 7. 13 and IS. By comparing Figs. 14(a) and 14(b) as well as 14(c) and 14(d)and the calculated precipitate radii (Schrems, 1991) for the HI and the LO-HI annealing, i t was found that the L O annealing leads to a 4ignificant acceleration of the precipitation process. If the initial oxygen concentrations are equal (data points C in Figs. 9, 14, 15) the additional LO annealing leads to a larger number of precipitates with smaller average size. when the curves i n Fig. 14 approach a quasi-stationary value. The additional precipitates observed in the LO-HI anneal (Fig. 14(d)) form during the LO annealing. but their growth rate during the LO anneal is small. Consequently, the precipitated fraction of oxygen remains very \mall (0-4 hr total annealing time in Fig. 14(b)). During the succeeding HI annealing the number of precipitates remains constant or decreases slightly (Fig. 14(d)).At the same time the precipitate radius (Schrems, 1991) grows significantly, which causes the reduction in the interstitial oxygen content found in Fig. 14ib). This illustrates why a L O and a succeeding HI anneal are frequently called nucletrrion crnnra/in,q and g r o ~ > t l az n t z r t r l i n ~ ~respectively. , From Fig. 14(c) and (d) an exponential dependence of the precipitate density on the value of the initial interstitial oxygen concentration and on the preceding anneals is appai-ent. This holds, even whcri the system approaches the quasistationary state. For the highest initial oxygen concentration (dashed lines in Figs. 14 and IS) an approach to the stationary state can be seen, while for the lower oxygen concentrations this was only observed for longer high-temperature annealing times than the value of 16 hr shown in the figures. In the initial phase of precipitation during the HI annealing, the average precipitate radius increases. while the critical radius (Fig. 15) increases at a much smaller rate (Schrems, 1991; Fig. 6.18). As the precipitated fraction (Fig. 14(h))approaches a value close to I , the critical radius almost reaches the value of the average radius. The increase of the critical radius leads to a gradual dissolution of an increasing number of larger sized precipitates, which now become subcritical. This dissolution process causes the temporary repopulation of smaller precipitate sizes observed in the calculated size-distribution function in Fig. 7, especially for 16 hr and 20 hr total simulation time. Those precipitates, which are larger than the critical radius. continue to grow. They consume the oxygen, which becomes available due to the dissolution of the smaller precipitates (coarsening). The growth rate (Eq. (20)) has now become very

422

M. SCHREMS

1.5

P Y

* ..-au 0.5

0.0

0

5

10

(4

time [h]

(b)

time [h]

15

20

FIG. 14. Precipitated fraction, (a) and (b), and precipitate density, (c) and (d), vs. total annealing time for A,, B , , C3 and A,, B , , C , from Fig. 9(b). (Schrems et al., 1989.)

10.

SIMULATION OF OXYGEN PRECIPITATION

1015 1014

108

10'

1015

r-r' '

'

Annealing: 750 c'/41i

1014

- 1013

10'

(d)

"

"

I

'

'

''1

+ 100OCC/16h

423

424

M . SCHREMS

(01: 5 s 10"cm 3 ) (0,: 8 0 10"cm ') ---c, 15 0 10"cna 1 ) -A,

8 4

(oAring. W. (1935). A t r t r . f'hys. (Leipzig) 24, 719. Bergholr. W . . Binns. M. J . . Booker. J . R . . Hutchinson, J . C.. Kinder. S. H . . Messoloras. S.. Nrwman. R . C . . Stewart. K J . . and Wilkes. J . G. (19891. Phil. Mng. B 59, 499. Binn\. M . J . . B r o u n . W. P . . Wilkes. J . G . . Newman. R. C . . Livingston. F. M.. Messoloras. S.. and Stewart. K. J . (19x3). Appl. f'/ry,\. Lrrr. 42, 5 2 5 . Bi-;+hec. I ' . . Schrems. M.. Hudil. M . . Potil. H . W . Kuhnert. W . . Pongratr. P.. Stmgeder. ( i . . and G r a s w b a u e r . M. lI9X9i. J ElwfrocI7rr7i. .Sot,. 136. 1542. Chtou. H . II9X7i.Solid Srtrrr 7 d i r r o l o q y (March). 77. Craven. K . A . (1981). I n Scmic.otidrrc / o r S / / i i , r v r , H. R . Huff. K . J . Kriegler and Y Takeishi 1. p. 254. ?-he Electrochemical Society. Pennington. N . J . . P . (1964). P/rv,\, R e \ . . il 133, 5x7. traundoii. P . . Fraundorf. G. K.. and Shimmini. F (1985). J . A p p l . Pliys. 58, 4049. Ereeland. P. E.. Jackson. K . A , . L.owe. (', W.. and Patel, J. R. (1977). A p p l . Phyt 1,err. 30, 31. . ( 1969). .SurJ .Scienc.v 14, 209. Ki5hino. S . . Matsushita. Y., Kanamori. M . . and lizuka. T. (1982). J p n . J . A p p l . Phys. 21, I.

446

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Landau, L . D., and Lifschitz, E. M. (1983). Lehrbuch der Theoretischen Physik, P. Ziesche (ed.), Vol. 10, Physikalische Kinetik, p. 458. Akademie Verlag, Berlin. Lavine, J. P., and Hawkins, G. A. (1986). In Oxygen, Carbon, Hydrogen and Nitrogen in Ciystalline Silicon. J. C. Mikkelsen, Jr., S. J. Pearton, J . W. Corbett and S. J. Pennycock (eds.), p. 301. Mat. Res. SOC.Symp. Proc., Vol. 59, Pittsburgh. Lavine, J. P., and Hawkins, G. A. (1989). In Atomic Scale Calculations in Materials Science. J . Tersoff, D. Vanderbilt and V. Vitek (eds.), p. 267. Mat. Res. SOC.Syrnp. Proc.. Vol. 141, Pittsburgh. Lavine, J. P., and Hawkins, G . A. (1992a). In Kinetics of Phase Transformations, M. 0. Thompson, M. Aziz, G. B. Stephenson and D. Cherns (eds.), p. 345. Mat. Res. SOC. Symp. Proc., Vol. 205, Pittsburgh. Lavine, J. P., and Hawkins. G . A. (1992b). In Strucfure and Properfies of Interfaces in Materials. W. A. T. Clark, C . L. Briant and U. Dahmen (eds.), p. 285. Mat. Res. SOC. Symp. Proc., Vol. 238, Pittsburgh. Lavine, J. P., Russel, J. T., and Hawkins, G . A. (1989). In Atomic Scale Calculations in Materials Science, J . Tersoff, D. Vanderbilt and V. Vitek (eds.), p. 261. Mat. Res. SOC.Synip. Proc., Vol. 141, Pittsburgh. Lifshitz, 1. M.. and Slyozov, V. V. (1961). J . Phys. Chem. Solids 35. Livingston. F. M., Messoloras, S., Newman, R. C., Pike, B. C., Stewart, R. J., Binns, M. J.. Brown, W. P., and Wilkes, I. G . (1984). J . Phys. C: Solid State Phys. 17,6253. Messoloras. S.,Newman, R. C., Stewart, R. J., and Tucker, J . H. (1987). Semicond. Sci. Techno/. 2, 14. Newman. R. C., Binns, M. J . , Brown, W. P., Livingston. F. M.. Messoloras, S., Stewart, R. J . , and Wilkes, J . G . (1983). Physica 116B, 264. Osaka. J.. Inoue, N., and Wada, K. (1982). J . Electrochem. Soc. 129, 2780. Pagani. M.,and Huber, W. (1987). In Proc. ESSDERC’87. P. U . Calzolari and G. Soncini (eds.), p. 339. TECNOPRINT, Bologna. Patel, J . R., Jackson, K . A., and Reiss, H. (1977). J . Appl. Phys. 48, 5279. Kavi, K . V. (1974). J . Electrochem. S o c . 121, 1090. Reiche, M.. and Nitzsche, W. (1985). Proc. Ist f n t . Autumn School on Gettering and Defect Engineering in Semiconductor Technology (GADEST), H. Richter (ed.),p. 174. Institute for Physics of Semiconductors, Frankfurt an der Oder, Germany. Schoeck. G.. and Tiller, W. A. (1960). Phil. M a g . 5 , 43. Schrems. M. (1991). Ph.D. thesis. Technical University of Vienna, Austria. Schrems, M . (1993). In Proc. o f the 5th Intern. Conf. on Shallow Impurities in Semiconductors, G . E. Murch (ed.),p. 231. Materials Science Forum, Vols. 117-118,Trans. Tech. Publ., Switzerland. Schrems, M., Brabec, T., Budil, M., Potzl, H., Guerrero, E., Huber, D., and Pongratz, P. (1989). Materials Science and Engineering B4, 393. Schrems, M., Brabec, T., Budil, M., Potzl, H., Hage, J., Guerrero, E., Huber, D., and Pongratz, P. (1990a). In Defect Control in Semiconductors, K . Sumino (ed.), p. 245. Elsevier Science Publishers B.V. (North Holland), Amsterdam. Schrems, M.. Budil, M., Hobler, G., Potzl, H., and Hage, J. (1991a). In Simulation of Semiconductor Devices and Processes, W. Fichtner and D. Ammer (eds.), Vol. 4, p. 113. Hartung-Gorre, Constance, Germany. Schrems. M.. Guerrero, E., Hage, J., and Potzl, H. (1991b). In the symposium on Advanced Science and Technology of Silicon Materials, Japan Society for the Promotion of Science. p. 40. Schrems, M., Hobler, G . , Budil, M., Potzl, H., and Hage, J. (1991~).Microelectronic Engineering 15, 57.

10.

SlMlJLAl ION O F OXYGEN PRECIPITATION

447

Schrema. M . . Hobler. G . . Potzl. H , and Hage. J lI99ld).I E E E K H M T '91 IEMT Symp..

p. 1 1 0 . Schrem, M . . Pongratr. P . . Budil. M., Potrl. H.. Hage. J . , Guerrero, E., and Huber. D. (IYWhl. In S[.rriic,onditc.tor S i l i c o n . H. R . Huff, K. G. Barraclough and J . Chikawa (ed\.). p. 144. The Electrocheniical Society. Pennington. N.J. Schrem.;. M.. Pongratr. P.. Budil. M . . f'otrl. H . . Hage. J . , Guerrero. E.. and Huber. 0. ( 1 9 9 0 ~ )I .n 7 h c Phvsic,.~c!fSenii~ondrtt for.\, E. M . Anastassikas and J . D. Joannopoulos (eds.). Vol. 1, p. 557. World Scientific, London. Seidman. D. N.. and Balluffi. R . W f l9h6). Phil. M u g . 13, 649. Stavola. M . . Patel. J . R . , Kirnrnerling. I . . C . . and Freeland. P. E. (1983). A p p l . P h y . Lett.

42. 73. Swaroop. K . . Kim. N . . Lin. W.. Hulli\. M . Shive. L.. Rice. A.. Castell. E . . and Christ. M . (1987). Solid Srare 7 w h r i o l o w v (March). 85. Tan. T. Y.. and Kung. C. Y . (1986). ./. A p p l . Phv.s. 59, 917. Taylor. W. J.. Jr. (1992). Ph.D. the\i\. [hike University, Durham. N.C. Tiller. W . A . . Hahn. S.. and Ponce. k-.A . (1986).J . A p p l . Phvs. 59, 3255. Tiller. W . A , . and Oh. S . (1988). J ,4pp/ P h v . ~64, . 375. Tmhev. S . . and Gutzow. I. (1972). k'ri.srtrll rtrid T ~ h r r i k7( 1-3). 4 3 . Turnbull. D.. and Fi5her. J . C. (1949) J ( ' h e m P h y s . 17, 71. Usami. T.. Matsushita. Y .. and Ogintr. M . (1984).J . Crysr. Growth 70, 319. Vanhellemont, J . . and Claeys. C. (19x7). J . Appl. Plly.5. 62, 3960. Vanhellemont. J . , and Claeys. C . (1988). Solid S / t i / r D r ~ , i c e sG. . Soncini and P. U . Calfolari (ed5.). p. 451. Elsevier Science Puhlijhrrs B.V. (North Holland), Amsterdam. van Kampen. N . G . ( 1981). .Sroc~hu.tricProc.~~s.sc~.v in Physk.c rind Chemisrry. North-Holland. .kn.;terdarn. Volrner. M.,and Weber. A . (1926) Zr\c h r . f'. Pliys. Chcm. 119, 277. Voronkov, V . V.. Mil'vidskii. M. G . . Grinshtein. P. M . , and Babitskii, Y . M . (1989). SOL.. PhyA. Crisrrrllo,qr.34(I).I 15. Wada. K.. and Inoue. N . (1985). J . C t v . \ l . Growth 71, II I. Wada. K . . Inoue. N.. and Osaka. J . (1983) M t i r . Re.\. Sot,. Sytnp. Proc-., Vol. 14, S. Mahajan and J. W. Corhett (eds.1. p. 125. El\evier, New York. Wada. K.. Nakani\hi. H.. Takaoka. t i . . and Inoue. N . f 1982). J . Ctysr. Growrh 57. 1535. Wagner. C. 11961). Z. Elekrroc.hc.ni. 65, 5 x 1 Wert. C . , and Zener. C . J . (19.50). J . A p p l . P h w . 21, 5. Wijaranakula. W.. and Matlock. J . t l 11991). J A p p l . Pliys. 69, 6982. Wilkes. J. G . (1983). J . Cp.sr. G'roit,tll 65. 214. I'ang. K . . Carle. J.. and Kleinhenr. K . 11987). J . Appl. Plivs. 62, 4890. Yatwtake. K . . CJnieno. M . . and Kawabe. H. 11984). Phvs. Slur. Sol. ( ~ I83. J 207. Zimmermann. H . , and Falster. K . ( 1992). 4 p p l . P/ivs. L e i / . 60, 3750.

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CHAPTER I 1

Oxygen Effect on Mechanical Properties K . Surnino anti I . Y o n t ~ n a g t r INSlITLITE FOR MATFRIAL9 R I \ E ARC t i TOHOKU CINIVFRSITY SLNDAI. JAPAN

INTRODUCTION . . . . . . . . . . . . . . . . . . PLASTIC DEFORMATION , \ N I ) I ~ X X A T I O NI SN SILICON CRYSTAI s . . . . . . . . . . . . . . . . . . . . 111. INFLUENCE OF DISP~RCI U O X Y G E N A r o M s ON THE MOBII.ITY OF DISLOCATIONS I N SII ICON . . . . . . . . . . . . . . I . Methodologic trl f'roblettr,s 111 t h e Mecrsuremeiit o f

450

. . . . . . . .

454 455

1. 11.

DiJloc,ution Veloc.itic,.\

2. V r l o c ~ i t yo f Disloc t i t r o n c 3. Velocity qf Disloc crtion 5

Iv.

V.

VI.

. . . . . . . .

.

.

in High-Purify Silicoir

rrr Silic.on Containing O.rvgen Itnpirriries . . . . . . . . . . . . . . . . . 4. Morphology c ~ f ' I ) r . s l o c . t r r i ~ ~ irn c r Motion . . . . . . . 5 . Interpretution the, O.r?gen k y ( f k / o n D i s l ~ c ~ t i ~ n Velocity . . . . . . . . . . . . . . . . . . . IMMOBIl.IZATION O F 1 ) 1 \ 1 ( H ATIONS B Y O X Y G E N . . . . . . I . Releuse Stre.\.s of I)r.cloc.trrion.\ fininobilized by Oxygen Imprrritirs . . . . . . . . . . . . . . . . . 2 . Sture of 0.rygen S ~ g r e g ~ oir t ~ Di.7loc.ation.s d . . . . EFFECT OF OXYGEN O N I)ISIOCATIONGENERATION . . . , I . Generation i f L ) ~ . ~ l o c ~ t r r r o n .s . . . . . . . . . . ?- 0.rvgen Efect oir l h s / o ( ~ u t i o n(ienerurion . . . . .

457

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460

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. . . .

463

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L>islocation-fre.e ( 'ns t i t / \ . . . . . . . . . . . . . 3 , O.rygen Effie I oir Mc,i /riirric.iil Properties of' Disloc~itrd

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. . .

.

. . . . . .

.

,

.

.

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. . . .

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469 4h9 412 414 414 416

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h l C I P I T A T I O N ON MECHAFilCAl

1 N F l l J E N C E OF O X Y ( , F I u

STRENGTH . . . . I . Getiercil Fetrtrcrr\

.

454

.

MI:.CHANICAL PROPERTII s cw SILI(.ON AS INFLUENCED B Y O X ~ G EIMPURITIES N . . . . . . . . . . . . . . . I . Mec,hunical Propertic\ ( J fHi,yh-Purity Silicon Crv,sttil.r 2 . O.rygeii Effie I O I I M(~c.lrutiic.ulProperties uf'

4. Theoreric~crlDerrL.ti/iori of- Yreld Churcrcreri.srics 5 . Wqfer .Srrengrhc~iriiigh v O t v q e n lmpiirities . .

45 I

. . . . . . . . . . . . . t h c ~.Sofrcrrring i d Silicoti Reluted Precipiturion ot O v t g ( ' i r , . . . . . . . . . . 2. Yield Strength of ('L-Sr w i t h O.rvg~iiPrecrpirtrrion . 3 . M e ( hnnisrrr o f P I c , i i ~ ~ i t u t i o.Sofieninx ii . . . . . 01

. .

4%)

fu . . . . . .

4%)

493 4%

449 Copyright cj I994 by Academi' Prer5. Inc All nghtr uf reproduction in any form re\erved ISHN 0 - 1 2 752142-Y

450

K. SUMINO A N D I . YONENAGA

VIII. EFFECTS OF NITROGEN A N D CARBON IMPURITIESON MECHANICAL PROPERTIES OF SILICON . . . . . . . . . . 1 . Nitrogen Effect . . . . . . . . . . . . . . . . . 2 . Carbon Effect . . . . . . . . . . . . . . . . . . IX. SUMMARY . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . .

499 499 504 507 5 10

I. Introduction

It is well known that wafers of Czochralski-grown silicon (CZ-Sij are much more resistive against the generation of dislocations or the occurrence of warpage than wafers of floating-zone-grown silicon (FZ-Sij during thermal cycling in device production processing. This is one of the main reasons why CZ-Si is used almost exclusively as the materials for VLSl or ULSI despite its lower purity compared with FZ-Si. It is natural to attribute such difference between CZ-Si and FZ-Si in the mechanical stability to the effect of oxygen impurities in CZ-Si on the dislocation processes occurring under stress at high temperatures. Oxygen impurities in CZ-Si are supersaturated in the temperature range below about 1250°C. Oxygen atoms in such a state effectively inhibit the dynamic activity of dislocations under stress. Supersaturated impurities naturally precipitate within a crystal when the crystal is held at temperatures at which the impurities move by diffusion at appreciable rates. Precipitation of oxygen in CZ-Si generally accompanies generation of various kinds of defects. Such defects are often reported to degrade the device function when they thread through device-active regions. They can also be utilized positively as effective gettering sites for harmful impurities incorporated by contamination. As to the effect on mechanical property precipitation of oxygen in CZ-Si leads to the softening of wafers. Understanding the effects of oxygen on mechanical properties of Si is, thus, very important in developing the production technology of Si devices. On the one hand, the mechanical properties of Si bear an important meaning also in basic study of crystal plasticity. The development of crystal growth technology in the last few decades has made it possible to grow Si crystals of high quality that are substantially free from dislocations. Dynamic properties of dislocations in Si have been studied experimentally in detail by observing the behavior of individual dislocations under stress, which were introduced intentionally into such high-quality crystals. Mechanical properties of Si measured by macroscopic mechanical tests can be analyzed on the basis of a microscopic model using the

1 1 . O Y Y - G I lu I I

I I ( 1 O N M E C H A N I C A L PKOPFRTIFS

45 1

dynamic properties of individual dislocations clarified in such a way. As it consequence, understanding the niacroscopically observed mechanical behavior of crystals in term5 of dislocation dynamics on a microscopic s a l e has now advanced the furthest in Si of all materials including impurity effects. This chapter reviews both the macroscopic and microscopic aspects of oxygen effects o n the mechanical behavior of Si. Effects of other light element impurities, such a 4 nitrogen and carbon, are also mentioned. Section 11 gives some basic aspect of plastic deformation of a crystal and also a brief description on the nature of dislocations in Si. Section I11 \bows the influence of oxygen atoms that dispersed within a Si crystal o n the dislocation motion. Section IV shows segregation of oxygen on dislocations and the resulting effect o n the dynamic activity of dislocations. Section V illustrates dislocation generation in Si as affected by oxygen. The experimental ol-wrvation is interpreted with the effect claritied in the preceding section. The effect of oxygen on macroscopic mechanical properties of Si I S described in Section V1. A description of the macroscopically observed mechanical behavior of Si crystals in terms of dislocation processes is also given there. Softening of Si caused by oxygen precipitation is described in Section VI1. Section VlIl gives the effects of nitrogen and carbon o n the mechanical strength of Si. 11. Plastic Deformation and Dislocations in Silicon Crystals

Si is completely brittle at low temperatures and becomes ductile gradually as the temperature is r a i d . This is common for all kinds of semiconductors. The temperature of the hrittlc to ductile transition can never be defined exactly. I t shifts to a high temperature when the crystal is stressed at it slow rate and shifts to ;I low temperature when stressed at a high rate. A rough measure for the tranbition temperature in Si may be taken to be about 500°C. All of w c h features reflect the dynamic property of dislocations in Si, which will be mentioned in later sections of this chapter. As in other kinds of diamond-type crystals, plastic deformation o f Si at high temperatures takes place hy means of a slip along the { 1 I I } planes in the ( I i0) directions. Such plastic deformation of Si by a slip is brought about by the glide motion of di\locations having t h e Burgers vectors of I!? ( I ( I i0) type, where (1 is the lattice parameter. along the { I 1 I } planes. During the plastic deformation of a crystal on a macroscopic scale, a high density of dislocations undergo glide motion at some appreciable velocity .

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K . SUMINO AND I . YONENAGA

To characterize the mechanical property, a crystal is usually subjected to a mechanical test by tensile or compressive deformation under a constant strain rate, and the so-called stress-strain curve is measured. In the case of a single crystal, the stress is referred to the shear stress component of applied stress, while the strain to the shear strain with respect to the slip system operating in deformation. The strain of a crystal consists of both elastic strain and plastic strain. The main part of the strain is elastic in the beginning of deformation of a crystal, namely, when the strain is small. Stress increases rapidly with increasing strain in such a deformation stage. After some amount of strain, plastic strain suddenly becomes predominant, and the stressstrain curve shows a break. This point is called the yield point. The stress at the yield point, called yield stress, is often taken as a quantity characterizing the mechanical strength of the crystal. The characteristics of the stress-strain curve of any crystal observed macroscopically are determined by a number of microscopic processes related to dislocations, such as generation, multiplication, motion, interaction with each other and with impurities. The basic equation which relates macroscopic deformation of a crystal with the dynamic state of dislocations inside it is given by ipl = NCb,

where 8,, is the plastic strain rate of the crystal, N is the density, V is the mean velocity, and b is the magnitude of the Burgers vector of dislocations in motion. The dislocation density is defined to be the length of dislocations contained in a unit volume of the crystal and has the dimension of c m - 2 . A dislocation in a Si crystal is energetically favorable when it lies along the most closely packed direction, which is one of the (1iO) directions. Thus, a stable dislocation in Si on the (1 11) plane is either a 60" dislocation o r a screw dislocation, which are the dislocation lines making the angles 60" and o", respectively, with the Burgers vector. Observations of dislocations by transmission electron microscopy have revealed that glide dislocations in Si are extended (Ray and Cockayne, 1971; Gomez, Cockayne, Hirsch and Vitek, 1975; Wessel and Alexander, 1977; Gomez and Hirsch, 1978; Foll and Carter, 1979; Sato and Sumino, 1979; Sato, Hiraga and Sumino, 1980). Namely, any such dislocations dissociate into two Shockley partial dislocations with the Burgers vectors of the (1 16) a ( 1 12) type, which bound a strip of stacking fault of the intrinsic type. The widths of the strip of stacking fault are 5.8 nm and 3.6 nm for a 60" dislocation and a screw dislocation, respectively, in Si (Gottschalk, 1979) under no stress. This means that such dislocations are

453

t I ( , . I . End-on high-resolution iniiigr\ of ( a ) ii in SI

cib\t,il

tSalo et

id..

h0' dislocation and ( b ) il screw dislocation

1980).

of a glide set. in the terminology o f Hirth and Lothe (1982). End-on high-resolution images of a 60" and a screw dislocation in Si are shown in Fig. 1 (Sato et a].. 1980). A dislocation loop generated f r o m ii source inside a crystal or a surface wurce assumes a shape of hexagon or half-hexagon, as shown schematically in Fig. 2 , when the di\lociition is isolated from other dislocations and the crystal does not contain a high concentration of impurities. 'The loop consist5 of segments of 60" dislocation and screw dislocation. The hO" segment consists of a 90' Shockley partial and a 30" Shockley partial hounding a strip of stacking fault. while the screw segment consists of two 30" Shockley partials. Atomic configurations at { h e core\ of a 30" Shockley partial and a 90" Shockley partial are shown in Fig. 3 . Geometrically, dangling bonds may

454

K. SUMlNO AND 1. YONENAGA

60° FIG.2. Schematic picture of a hexagonal-shaped dislocation loop on the ( I 11) slip plane in Si crystal. The hatched region shows stacking fault of intrinsic type.

be aligned along the dislocation core. However, such geometrical dangling bonds are now believed to be reconstructed to form bonds between two neighboring atoms along the dislocation line on the bases of electronic state of dislocations and theoretical calculations. A review on the dynamic behavior of dislocations and the characteristics of plastic deformation in various kinds of semiconductors is given by Sumino in a forthcoming issue of the Handbook on Semicouductors (North-Holland). 111. Influence of Dispersed Oxygen Atoms on the Mobility of

Dislocations in Silicon 1 . METHODOLOGICAL PROBLEMS I N THE MEASUREMENT OF

DISLOCATION VELOCITIES

Many papers have so far reported experimental results on dislocation velocities in Si as functions of stress and temperature. In most works dislocation velocities have been measured by means of intermittent technique; namely, the positions of dislocations are determined at room temperature by the etch pit technique or X-ray topography, while they are displaced by stress at elevated temperature. The intermittent technique has several origins for error in determining the accurate velocity of dislocations as pointed out by Sumino (1987). The most important and unavoidable origin of the error is the immobilization of dislocations by impurities. As demonstrated later, dislocations in a crystal act as very effective

1 1.

O X Y G E N F I t F( 1 ON ME C HANIC A 1 PKOPERTIES

455

(b)

(a)

F I G .3. Atomic configuration\ a l Ihe coi-es of (a1 a 30" Shockley partial dislocation and Ib1 >I 9 0 Shockley partial dislocation in 51crystid.

gettering sites for impuritie\ at elevated temperatures. Dislocations are locked when they getter impurities. In some cases t h e effect brings about ;L critical stress to start dislocations moving. In other cases a locked dislocation spcnds some incubation period before starting after application of stress. In the latter c a w the stress dependence of t h e dislocation velocity is measured to be htronger than the real one. Impurities are incorporated into the crystal with various origins, as residual impurities or by contamination. Dislocation\ are unavoidably held at rest at elevated temperatures in the intermittent technique. which leads to gettering of impurities by the dislocations. Thus. it is difficult to obtain the velocity of dislocation in motion avoiding the locking effects by impurities in the intermittent method. 'The most reliable experimental technique for measurements of dislocation velocity is thought to be that by means of in situ X-ray topography developed by the Sumino group (Sumino and Harada. 1981; lmai and Sumino, 1983) utiliLing a high-power X-ray source. a high-temperature tensile stage. and a highly sensitive T V system. Motion of isolated dislocations in a crystal introduced from some sources can be followed by real time observation as functions of the temperature and the applied stress with this technique. 'The technique is free from the ambiguity related to the locking effect o f irnpurities in determining the dislocation velocity.

2 Vtmcirv

OF

DISLOCATION\ I N HILH-PURITY SILICON

F i i \ t . experimental datd o n velocitie4 of di\locatlon\ i n a high-purity FZ-Si cry\tal are \hewn. The velocitie\ of i\olated 60"and \crew di\loca-

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K . SUMINO AND 1. YONENAGA

tions at various temperatures measured by means of the in situ X-ray topographic technique are plotted against the shear stress in Fig. 4(a) (Imai and Sumino, 1983). Figure 4(b) shows the dislocation velocities under various stresses plotted against inverse temperature. It is seen that the velocities of the both types of dislocations in high-purity FZ-Si are linear with respect to the shear stress in the stress range 1-40 MPa and that the activation energies are independent of the shear stress in the temperature range 600-800°C. The dislocation velocity v is expressed well with the following equation: u =

v,,(7/To)exp(- Q / k , T ) .

(2)

The magnitudes of u,, are 1.0 x lo4 and 3.5 x lo4 m/s and those of Q are 2.20 and 2.35 eV for 60" and screw dislocations, respectively (Imai and Sumino, 1983). The shape of moving dislocations is observed to be a regular hexagon or a half-hexagon. The stress exponent of u has been determined to be higher than unity by various groups with the intermittent technique, ranging from 1.2 to 1.4, or not to be constant but to depend on the stress range where the measurements were conducted (Suzuki and Kojima, 1966; Patel and Freeland, 1967; Erofeev, Nikitenko and

3

FIG.4a. Dislocation velocity in high-purity FZ-Si crystal plotted against shear stress for various temperatures (Imai and Sumino, 1983).

1 1.

OXYGEN t t FFC T ON MECHANICAL PROPERTIES

457

2 1 0 ~ ,1 ~K"

t-'icl. 4b. Di\localion velocity in high-puritv FZ-Si crystal plotted against i n v e n e temperashear \tre\,s (Irnai ,ind Surnino. 1983).

tui-t' t'm barious

Osvenskii. 1969; George, Fscavarage. Champier and SchrBter. 1972: Fisher, 1975, 1978). The resulls obtained with the intermittent technique are not in quantitative agreement among different groups. Such disagreement may be attributed to the drawback involved in the intermittent technique.

3.

VEL.OC17 Y 01'DISLOCATIONS I N sII.ICON

CONTAINING OXYGEN

I M P U K I l IES

Figure 5 shows the relations between the velocity of a 60" dislocation and the shear stress at various temperatures in a Si crystal containing oxygen impurities at a concentration o f 7 . 4 x lo" atomsicm' obtained by means of the in situ X-ray topographic technique (Imai and Suniino, 1983). Data for high-purity FZ-Si are also shown in the figure. Dislocations in the crystal containing oxygen impurities move at velocities that are equal to those in the high-purity FZ-Si crystals in a high-stress range. However, dislocations originally in motion under high stress cease to move when the stress is reduced t o lower than about 3 MPa in the Si crvstal containing oxygen impurities. 'The velocity of dislocations in the crystal containing oxygen decreases more rapidly t h a n in the high-purity

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K . SUMINO AND I . YONENAGA

0

0

High purity FZ 101 Z4x10'5m-3

I I

1

/

732°C

'

I 10

Shear stress,

I

1c MPa

FIG.5 . Velocity versus shear stress relations at various temperatures of 60" dislocations in a Si crystal containing oxygen impurities at a concentration of 7.4 x 1017 atomsicm'. Open circles indicate the data for high-purity FZ-Si (lmai and Sumino, 1983).

FZ-Si as the stress is decreased toward such a critical stress for the cessation of dislocation motion, shown by vertical broken lines in the figure. The stress exponent of the dislocation velocity is determined to be apparently larger than unity in the low-stress range in such a Si crystal. Figure 6 shows the velocity versus stress relations for 60" dislocations at 647°C in Si with dissolved oxygen impurities at various concentrations (Imai and Sumino, 1983). Broken lines drawn vertically bear the same meaning as those in Fig. 5, namely, the critical stresses below which dislocations originally moving under a high stress become immobile. Again, the dislocation velocities in the crystals containing oxygen impurities at a n y concentration are almost the same as those in high-purity FZ-Si under high stress. Both the deviation of the velocity from that in the high-purity FZ-Si with decreasing stress in the low-stress range and the critical stress for the cessation of dislocation motion increase with an increase in the concentration of dissolved oxygen impurhes. The magnitudes of the critical stress for the cease of dislocation motion are shown in Table I for Si crystals containing the various types of impurities.

OXYGLN F l l € ( I ON M L C H A N I C A L

10

PROPFKTIF5

459

-

Shear stress,

1c I

MPa

Fic;. 6. Velocitv v e r w s shear p*). In situ observations of dislocation multiplication processes by means of X-ray topography (Sumino and Harada, 1981) and transmission electron microscopy (Sato and Sumino, 1977; Sumino and Sato, 1979) have revealed that dislocation multiplication takes place by two basically different mechanisms in Si crystals: one is spontaneous multiplication of gliding dislocations, for example, by means of double cross slip and the other multiplication through interaction of dislocations belonging to different slip systems. The multiplication rates of dislocations of the primary and secondary slip systems are then given by dN,ldt

=

K N l ~ l ~ e f+f ,K, * N I N : ! v I T ~ ~ ~ , I ,

( 18a)

dN,ldt

=

K N 2 v 2 ~ e K+, 2K * N 2 N I v 2 ~ e f f , 2 ,

(18b)

respectively, where K and K* are constants that characterize the two multiplication processes. Stress-strain curves calculated with Eqs. (16) through (18) are shown in Fig. 25, which is in good agreement with experimental observations shown in Fig. 18. Figure 26 shows the calculated upper and lower yield stresses with solid lines as functions of various parameters. Experimental data are shown by open and filled circles. The agreement between calculation and experiment is excellent. b. Effect of Dislocation Locking by Oxygen Impurities

We have seen in Sections VI.2 and 3 that an increase in the oxygen concentration in Si results in a significant increase of the strength of the

11

OX’rCrFlu t l I t ( I O N MF( H A N I C A L PROPtRTIF\

900°C I .L I 5 10 IS Shear strain

30

r--

o/o

-

485

L

I I 10 15 Shear strain , ‘lo

5

~

T- 600°C

Shear strain, Yo (C)

Fiti. 7 5 . Calculated \li-e\\-\trdin ctine\ o f high-purity si crystals a\ dependent o n ( a ) temperature. (h) sheai- strain rate ,ind I C ) initial density of dislocations. which corre\pond t o experimental strea\-strain curve\ in Fig. I X ( a ) . ( b ) . and ( c ) . respectively (Sumino and Yonenaga. 1993).

486

K . SUMINO AND 1. YONENAGA

T , 'C 850

800

L 0.85 0.9 0.95 1 0 3 / ~ K-' ,

1 10-5

10-4 € , s-'

Ir 3

(b)

E

-

0

lo4

105 lo6 N o , cm-2

107

(C)

FIG.26. Upper yield stress T , and ~ lower yield stress T , of ~ high-purity Si crystals as dependent on (a) temperature, (b) shear strain rate and ( c ) initial density of dislocations. Solid lines show the results of calculation while open and filled circles show experimental points for T~~ and T , ~ ,respectively (Sumino and Yonenaga, 1993).

crystal only when the crystal is initially dislocated. We have concluded that the strengthening of Si crystals due to oxygen impurities is not related to the resistance of oxygen atoms dispersed within the crystal against the dislocation motion but to the locking of dislocations due to the segregation of oxygen atoms on the dislocation core. Here, we discuss how such locking of dislocations affects the yield behavior of the crystal. Let us consider a simplified case in which dislocations of only the

II

O X Y G E N Et I-f

(

I O N M F C H A N I C A L PROPFRTltS

487

primary slip system are activated in deformation and they multiply themselves, being controlled by Eq. ( 1 5 ) . Suppose that the applied stress T , , increases at a constant rate q ; namely. T , = q t . When the dislocation density N is low enough that T , in Eq. ( 14) is much lower than T,,.~. T , , is approximately equal to T,,,. Assuming that all dislocations in the crystal are in motion. Eqs. (13) and ( 15) lead to N as a function of^,, to be given as follows (Sumino. I989a): N

=

N,,exp(/cm' that contain didocations at various densities shown in the figure ( i n cm :) in deformation at 800°C under a shear \train rate of I x IW4 5 - ' .

FK,.44. Upper yield stress T " , of carbon-doped FZ-Si and CZ-Si crystals with dislocation densitieb of about I x loh c m - ' plotted against the concentration 0 , of dissolved oxygen atoms. Open circles are the dala for carbon-lean Si. Filled marks are for carbon-doped Si at the carbon concentrations shown in thc figure. The upper yield stresses are for defcormation at X(WC and 900°C under a shear strain rate of I x s (Yonenaga and Sumino. 1984).

'

506

K . SUMINO A N D I . YONENAGA

-

0

0

1 2 3 4 Ic, 1 , 10‘ 7 a t 0 ~ i i 3

FIG.45. Upper yield stress T , and ~ lower yield stress T , of ~ CZ-Si crystals with dislocation densities of about 1 x lo6 cm-? and dissolved oxygen concentrations of about 6 x lo” cm-’ plotted against the concentration C , of dissolved carbon atoms. The yield stresses are for deformation at 800°C and 900°C under a shear strain rate of 1 x s - ’ (Yonenaga and Sumino. 1984).

bon-lean CZ-Si plotted against the oxygen concentration for deformation at 800°C and 900°C (Yonenaga and Sumino, 1984). Data for usual FZ-Si and carbon-doped FZ-Si crystals are also shown. The initial densities of dislocations in all the crystals are about 1 x lo6 ern-'. Open circles and solid lines are the data for carbon-lean FZ-Si and CZ-Si (Yonenaga et al., 1984). Filled triangles, circles and squares are for CZ-Si doped with carbon at concentrations of 0.9 x lOI7, 1.7 x loi7and 2.5 x lOI7atoms/ cm’, respectively. It is seen in the figure that carbon impurities at concentrations of the order of lOI7 atoms/cm3 have almost no influence on the magnitude of upper yield stress of Si crystal when the concentration of oxygen is lower than about 4 x 1017 atoms/cm3. However, the upper yield stress is enhanced distinctly by the presence of carbon impurities if the crystals contain oxygen at concentrations higher than about 5 x loi7atoms/cm3. Figure 45 shows the upper and lower yield stresses of CZ-Si crystals at 800 and 900°C plotted against the concentration of carbon atoms (Yonenaga and Sumino, 1984). All the crystals are dislocated at densities of about 1 x lo6 cm-* and contain oxygen at concentrations of about 6

I 1.

OXYGEN E l I F C 1 ON M F C H A N I C A L PROPERTIE5

507

x lo” atoms/cm3. The upper yield stress increases monotonically with increase in the carbon concentration. Carbon atoms dissolved at a concentration of 2.5 x IO” atomsicrnj enhance the upper yield stress of the crystal by a factor of 1.4. From these results, it is concluded that carbon impurities bring about the increase in mechanical strength of silicon crystals if they coexist with oxygen impurities the concentration of which is higher than about 5 x l o ” atoms/cm’. Since it has been clarified from direct measurements (Sumino and Lmai. 1983) that carbon impurities by themselves have no appreciable effect on the dynamic property of dislocations. carbon atoms in CZ-Si are thought to promote the dislocation locking due to oxygen atoms. It is conceivable that such promotion of dislocation locking is caused by carbon atoms that are incorporated in the core region of a dislocation and act as the preferential nucleation sites of oxygen clusters. IX. Summary

The characteristics in mechanical behavior of a Si crystal on a macroscopic scale are determined by dynamic processes of dislocations in the crystal that take place on a microscopic scale under stress. Important among such processes are the generation, multiplication and motion of dislocations as well as interaction of dislocations with each other. The effect of oxygen on mechanical properties of Si is interpreted in terms of knowledge on how oxygen impurities affect such dislocation processes. Difficulty appears in measuring the dislocation velocity when oxygen impurities are dissolved in Si. ‘This is related to immobilization of dislocations caused by segregation of oxygen atoms on the latter. The difficulty has been overcome by adopting the technique of in situ X-ray topographic observation . Dislocation mobility in Si increases very rapidly as temperature increases. The dislocation velocity in high-purity FZ-Si depends on the stress linearly down to a very low stress. The linear dependence of the dislocation velocity on the stress holds also in Si containing oxygen impurities at a concentration of the level in CZ-Si when a dislocation moves at a rather high velocity under a high stress. The dislocation velocity in CZ-Si under such a high stress is the same as that in high-purity FZ-Si. On the other hand, the dislocation velocity in Si containing oxygen impurities is lower than that in high-purity Si when the dislocation moves at a low velocity under a low stress. The retardation of dislocation motion caused by oxygen impuritie\ is accompanied by the disturbance in the shape of moving dislocations. Under a stress lower than some critical

508

K . SUMINO A N D I . YONENAGA

stress, a dislocation ceases to move in Si containing oxygen impurities. The magnitude of the critical stress for cessation of dislocation motion increases with an increase in the oxygen concentration. Such observations together with theoretical analysis lead to the conclusion that oxygen atoms individually dispersed in a Si crystal do not affect the dislocation velocity in the concerned temperature range. However, they catch up to slowly moving dislocations and develop clusters on the dislocation line. The development of oxygen clusters results in the perturbation in the line shape and retardation of the dislocation in motion. An originally fresh dislocation is immobilized in Si containing oxygen impurities when it is halted at high temperatures under no applied stress. A theoretical treatment shows that the immobilization of dislocation is caused not by the development of the Cottrell atmosphere of oxygen atoms around the dislocation but by the development of clusters of oxygen atoms on the dislocation line. Oxygen atoms or, more generally, impurity atoms are gettered by dislocations by means of (1) preferential nucleation of precipitates of supersaturated impurities on the dislocation line or (2) some special reaction that takes place at the dislocation core to incorporate impurity atoms from the matrix region. Oxygen impurities effectively suppress the dislocation generation in Si under stress. The mechanism of suppression is closely related to the generation process of dislocations in a Si crystal. Dislocations are generated heterogeneously from some structural irregularities in the crystal under stress. Surface damage in a Si crystal such as scratches and indentations acts as effective generation centers for dislocations. Small amorphous Si regions are developed around such damages made at room ternperature. Such an amorphized region recrystallizes into a dislocated region when the crystal is brought to high temperatures. Dislocations come out of such a region and penetrate into the matrix if the crystal is under stress, leading to the dislocation generation. Dislocation generation from the damaged region takes place even under a very small stress in high-purity FZ-Si. However, dislocations are not generated under stresses lower than a certain critical stress in CZ-Si. This is caused by the locking of dislocations in the recrystallized regions due to gettering of oxygen atoms while the crystal is heated up. The yield strength and stress-strain characteristics of Si are well understood on the basis of a theoretical model using various dislocation processes observed in experiments. Oxygen impurities give no appreciable influence on the mechanical strength of Si if the crystal is initially free from dislocations. The oxygen effect appears in initially dislocated Si crystals. Oxygen impurities in Si give rise to the same effect on mechani-

11.

OXYGEN E r t t ( I

o~

ME( H A N I C A L PROPERTIFS

509

cal behavior a s the decrease in the density of dislocations initially contained in the crystal does. These are successfully described with the theory by taking account of the locking of dislocations by oxygen impurities. The high resistance of CZ-Si wafers in comparison with FZ-Si wafers to warpage due to thermal cycling is well interpreted with the idea of dislocation locking by oxygen impurities. Precipitation of supersaturated oxygen in Si results i n a decrease in the mechanical strength. The mechanical behavior of a precipitation-softened Si crystal is very similar to that of a Si crystal with a high density of dislocations initially contained in the crystal. Dislocations punched out from precipitate particles act a s dislocation sources and bring about the reduction in the yield strength of the crystal. Dissolution of precipitates in precipitation-softened Si at high temperatures results in restoration of the high yield strength. Nitrogen impurities in Si effectively immobilize dislocations even though nitrogen atoms dispersed within the crystal have no appreciable effect o n the velocity of dislocations in motion. The immobilization of dislocations is related to gettering of nitrogen by the dislocation core. The strength of locking per one nitrogen atom is about 30 times higher than that of an oxygen atom. Nitrogen impurities enhance the yield Ytrength of a Si crystal when the crystal is initially dislocated. It does not give rise t o precipitation softening due to annealing at temperature around 1 ooooc.

Carbon impurities in Si at concentrations up to I x 10’’ atomsicm’ do not give rise to any appreciable effects on both dislocation mobility and yield strength. However, they enhance the mechanical strength of Si when they coexist with oxygen impurities. Oxygen impurities in Si are amphoteric in nature from the view of its effect on the mechanical strength. Oxygen atoms individually dissolved in Si enhance the mechanical stability of Si at elevated temperatures. This effect originates from gettering of oxygen atoms by dislocations. which leads to immobilization of the dislocations. The effect becomes increasingly remarkable as the oxygen concentration in Si increases. On the other hand, precipitation of supersaturated oxygen impurities accompanies the generation of defects that act as dislocation sources and leads to the softening of Si. However. such precipitation-related defects can be effectively utilized as gettering sinks for heavy metallic impurities in device production technology. In conclusion. i t is empha\ired that defect control in Si technology is most effectively accomplished on the basis of correct understanding of oxygen effects on various dislocation processes in Si.

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REFERENCES Abe. T., Kikuchi, K., Shirai, S . , and Muraoka, S. (1981). In Semiconductor Silicon, H. R. Huff, J . Kriegler, and Y. Takeishi (eds.), p. 54. Electrochem. Soc., Princeton. N.J. Clarke, D. R.,Kroll, M. C., Kirchner, P. D., Cook, R. F . , and Hockey, B. J. (1988). Phvs. R e v . L e t t . 60, 2156. Doerschel, J.. and Kirscht, F.-G. (1981). Phys. Stat. Sol. ( a ) 64, K85. Eremenko. V., and Nikitenko, V. 1. (1972). Phys. Stat. Sol. ( a ) 14, 317. Erofeev. V . N., Nikitenko, V . I . , and Osvenskii, V . B. (1969). Phys. Stat. Sol. 35, 79. Fisher, A. (1975). Expl. Tech. Phys. 23, 617. Fisher, A . (1978). Kristall und Technik 13, 1217. Foll. H.. and Carter, C. B. (1979). Philos. M a g . A40, 497. George, A , , Escavarage, C., Champier, G.. and Schroter, W. (1972). Phys. Stat. Sol. f b ) 53, 483. Gomez, A , , Cockayne, D. J . H., Hirsch, P. B., and Vitek, V. (1975). Philos. M a g . 31, 105. Gornez. A , , and Hirsch, P. B. (1978). Philos. M a g . A38, 773. Gottschalk, H. (1979). J. Physique 40, C6-127. Gridneva, I. V., Milman. Y. V., and Trefilov, V. I. (1972). Phys. Stat. Sol. ( a ) 14, 177. Hirth, J . P., and Lothe J . (1982). Theory of Dislocations. John Wiley & Sons, New York. Imai. M . , and Sumino, K. (1983). Philos. M a g . A47, 599. Kayano, H. (1968). Trans. Jpn. Inst. M e t . 9, 156. Kishino. S.. Matsushita, Y., Kanamori, M., and lizuka, T. (1982). Jpn. J . Appl. Phvs. 21, I . Koguchi, M . . Yonenaga, I . , and Sumino, K. (1982). Jpn. J . Appl. Phys. 21, L411. Leroueille. J . (1981). Phys. Stat. Sol. ( a ) 67, 177. Louchet. F. (1981). Philos. M a g . A43, 1289. Mahajan, S . . Brasen, D., and Haasen, P. (1979). Acta Metall. 27, 1165. Minowa. K.. and Sumino. K. (1992). Phys. R e v . Lett. 69, 320. Patel. J . R. (1964). Discuss. in Furaday Soc. 38, 201. Patel, J. R . . and Chaudhuri, A. R. (1963). J . Appl. Phys. 34, 2788. Patel, J . R., and Freeland, P. E. (1967). Phys. R e v . B 13, 3548. Peissker, P., Haasen, P., and Alexander, H. (1961). Philos. Mag. 7, 1279. Ray. 1. L. F.. and Cockayne, D. J. H. (1971). Proc. R o y . Soc. A325, 543. Sato, M.. Hiraga, K., and Sumino, K. (1980). Jpn. J. Appl. Phys. 19, L155. Sato. M.. and Sumino, K. (1977). Proc. 5th Int. Conf. on High Voltage Electron Microscopv. p. 459. Sato. M., and Sumino, K. (1979). Kristall und Technik 14, 1343. Sato, M., and Sumino, K. (1985). In Dislocations in Solids. H. Suzuki, T. Ninomiya, K . Surnino and S . Takeuchi (eds.), p. 391. University of Tokyo Press, Tokyo. Schroter. W . , Brion, H. G . , and Siethoff, H. (1983). J . Appl. Phys. 54, 1816. Seeger. A . (1958). In Handbuch der Physik V11/2, S . Fliigge (ed.), p. 114. Springer, Berlin. Siethoff. H . . and Haasen, P. (1968). In Lattice Defects in Semiconductors, R. R . Hasiguchi (ed.). p. 491. University of Tokyo Press, Tokyo. Stickler, R., and Booker, G. R . (1963). Philos. M a g . 25, 1429. Suezawa, M . , Surnino, K., and Yonenaga, 1. (1979). Phys. Srar. Sol. ( a ) 51, 217. Sumino, K . (1986). Muter. R e s . Soc. Symp. P r o c . , Vol. 59, Oxygen, Carbon, Hydrogen and Nitrogen in Crystalline Silicon, J. C. Mikkelsen, Jr. (ed.), p. 369. North-Holland, New York, Amsterdam and Oxford. Sumino, K . (1987). Proc. 7th Inr. School on Defects in Crystals, E. Mizera (ed.) p. 495 World Scientific, Singapore.

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Surnino, K . (198%). M u t e r . Sci. E n g . 84. 3 3 5 . Surnino. K. (1989b). I n Point und b,’.rrc,nclcd Dc;fi.cts in Semic~o,7duc./or.s.G . Benedek. A . Cavallini and W. Schroter ( e d \ . ) .p. 77. Plenum Press, New York and London. Surnino. K. ( 1992). In P r o ( . . lsr Puc.ific RIM Internail. Conf. oti Advunc.ed Muteriuls und Proc,e.s~ting,C. Shi. H. Li and A . Scott (eds.). p. 49. The Minerals. Metals & Material.; Soc.. Warrendale. P.A. Sumino. K., Harada, H..and Yonenaga. I . ( I Y X O ) . J p n . J . Appl. Phy.~.19, L49. Sun~ino.K., and Harada. H. (1981). phi lo^. Mtrg. A44, 1319. Suniino. K . . and Irnai. M . (1983). P / i i l ( ~ aMtrg. . A47, 753. Surnino. K.. and Sato. M . (1979). Krr.sttr// r r ! 7 d Icclrnik 14, 1343. Sumino. K . . and Yonenaga. I . ( 1991 .Yo/rd Stcrtc’ Phenotnenu lYi20. Gettering trnd l)efr,c/ Etigineering in .Semiccindrrc./or I , c . h t i ( ~ l ~Y gl . ~M. Kittler and H.Richter (eds.). p. 295. Sci-Tech Publication. Liechten\tein Sumino. K . . and Yonenagn. 1. (1997). fJ/iv.s. S t u t . Sol. f u ) . 138, 573. Sumino. K . . Yonenaga. 1.. Irnai. M . arid Abe. T. (1983). J . Appl. Pl7vs. 54, 5016 SuLuki. T.. and Kojinia. H.(1966) 4 c . t ~Mutull. 14, 913. Tokurnaru. Y., Okushi. H..Masui. T . . and Abe. T (19x2). J p n . 1.A p p i . P k v s . 21, L443. We<sel. K., and Alexander. H . (1977). Philo.\. Mtrg. 35. 1523. Yawtake. K . . Urneno. M.. and Kawabe. H.(1980).Appl. Plivs. Lctr. 37, 789. Yasutake. K . . Urneno. M . . and Kawahe. H.(19x2). Ph.vs. Stut. Sol. fu) 69, 333, Yonenaga. I . . and Surnino, K . (1978) !%v,\. S l u t . Sol. f u ) SO, 6x5. Yonenaga. I . , and Surnino, K . (19x2). Jpn J . A l ~ p l .Phys. 21, 47. Yonenaga. 1.. and Surnino. K. (19x4). J p n . J. 4ppl. P h y s . 23, LS90. Yonenuga. 1.. and Sumino. K. (1980. In I)is/oc.eirions i n Solids. H.Suzuki, T. Ninomiya. K. Sumino and S . Takeuchi ( r d s . ) . p 385 University of Tokyo Pres5. Tokyo. Yonenaga. I.. Suniino. K.. and Ho\hi. K (1984). J . A p p l . PAy.5. 56, 2346.

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SEMICONDIII IOKS A N D S E M I M E T A L S . V O L 42

C H A P T E R 12

Grown-in and Process-Induced Defects W. Ber direction (Fig. 10); Small circular extrinsic stacking faults of non-1/3 < I 1 I > type (Fig. 2d. Bergholz, Hutchison and Pirouz, 1985); Dark spot defects (Fig. 9); Ordinary 60" dislocation (which nucleate on oxygen precipitates; Tempelhoff et at., 1970).

FIG.2. Secondary defects associated with oxygen precipitation: (a) '/I < I II>-type stacking faults (SFs) delineated by Secco defect etching o f a { 110) cleavage plane in the hulk of a Si-wafer (SFs that are Liewed end-on are denoted as SFe. those that are inclined to the cleavage plane are denoted as SFil; ( h ) prismatically punched dislocation loops delineated by Secco defect etching. etched surface i s the (100) wafer surface, the loops are marked by arrow heads: (c) prismatically punched dislocation loops delineated by Secco defect etching, etched surface i s a (I10) cleavage plane; (d) small circular extrinsic stacking fault o f a non-'/x< I I 1 >-type (high-resolution lattice image. the extra {III} plane is marked by arrow heads. Bergholz et al., 19851.

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GROWN-IN A N D PROCESS-INDUCED DEFECTS

52 1

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W . BERGHOLZ

2. FACTORS THATDETERMINE THE TYPEOF OXYGEN PRECIPITATE u . Volume Expansion

The key to this puzzling scenario is the fact that the formation of SiO, precipitates is accompanied by a volume expansion of about a factor of 2. In other words, the space taken up by one Si atom increases by a factor of 2 as the Si is transformed into S O , (Bourret, Thibault-Desseaux and Seidmann, 1984). b. Surface, Elastic, and Chemical Energies (Tiller, Hahn and Ponce, 1986)

To accommodate this additional volume the crystal can respond in different ways, which are depicted schematically in Fig. 3: Precipitate + intrinsic defect

v v A A

FIG.3. Schematic representation of the size of the surface energy E S ,of the elastic energy

.

E,, chemical energy E, (from the formation of self-interstitials) and the ratio of the volume

of the precipitate (which is a measure of the number of oxygen atoms removed from supersaturated solution) to the surface as a function of temperature and of the predominant defect in that temperature range. The first three quantities make the precipitate nucleation more difficult (symbolized by a minus sign), whereas the larger is the ratio volume/surface, the larger is the gain in chemical energy in relation to the energies in connection with the surface. The shape of the oxygen precipitates are drawn as open figures in the RHS of the figure, the intrinsic defects agglomerates are hatched. The triangles represent the stress of the Si-matrix on the precipitate.

12.

GKOWN-IN 4")

PKOCESS-INDUCED DEFECT5

523

Lattice strain. which puts the growing precipitate under compressive stress, at t h e expense of elastic energy E,, (both of the crystal and the precipitate); 'To reduce the strain, the precipitate can, in principle, assume a shape that reduces the strain (e.g., platelike instead of spherical morphology. at the expense of surface energy E , ): The growing precipitates can push Si-atoms onto interstitial sites. Thus. Si self-interstitial\ are created, at the expense of additional chemical energy E,; T o reduce the chemical energy, the self-interstitials can agglomerate to extended intrinsic defects (e.g., stacking faults). which. of course is not "free of charge" either. but entails formation energy E, for these defects. The whole process is driven by the tendency of the crystal to reduce i t x total energy E,,,:

EtL,,= E,, t t,,t E ,

+

E,

+ E,.

where E,, is the energy of solution for the dissolved oxygen precipitate.

c . Kiri 6)tics Which of the various precipitate types and secondary defects are formed depends not only on the energies involved. but, to a considerable extent, on the kinetics of the process: 0

0

The transport of oxygen atoms to the precipitates. i.e., the oxygen diffusion coefficient; The transport of self-interstitials away from the precipitates. the diffusion coefficient of %elf-interstitials

Just to give an example. the growth of ribbonlike precipitates may be favoured at low temperatures. where the oxygen diffusion coefficient is small due to the large migration enthalpy of 2.5 eV. This can be understood by the fact that the precipitate keeps growing into regions in which no oxygen precipitation has taken place; i.e., in a way the precipitate moves to the oxygen atoms rather than the atoms to the precipitate (Fig. 4). In the end. only small cylindrical regions around the principitate have been depleted of oxygen.

d . 7he Rolt) oj'lntvinsic Poitit I 1 i ~ f t ~ c ~tirid t . v Stwindrivy Dqfects As mentioned under b, the emission of self-interstitials (or the absorption of vacancies) is a n important avenue for the crystal to satisfy the

Z 1 0 H 9 8 3 9 'M

PZS

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525

particular, if oxygen precipitates act as nucleation centers for such defects. Figures 2b. 2c and 6 are examples for such a situation. From the high-resolution TEM images o f a large number of oxygen precipitates formed after annealing at 750°C. it could be concluded that a large percentage of the precipitates had a stacking fault attached to them (Bergholz et al.. 1989a). In fact, it appears worth mentioning that a similar coexistence of impurity atom precipitates and stacking faults as a sink for intrinsic defect has been reported by Seibt (1990) for Cu in Si; i.e.. such a state of affairs seems to be quite typical for the precipitation in silicon

FIG.5 . Lang X-ray topograph of ii typical IS0 m m wafer after a standard device process. The bright rings are regions of strong oxygen precipitation. the dark rings are area\ o f retarded oxygen precipitation. (The feature5 opposite the wafer flat are dislocations cauzed by the \lits in the quartL wafer boat\.)

526

W . BERGHOLZ

FIG. 6. High-resolution TEM micrograph of a platelike oxygen precipitate on {loo} with a stacking fault on { I 1 I} attached to it. The orientation of the stacking fault plane is marked.

and is presumably ultimately due to the properties of self-interstitials (equilibrium concentration and diffusion coefficient at low and medium temperatures).

3, OXYGEN PRECIPITATION I N DIFFERENT TEMPERATURE REGIMES It is the aim of this subsection to bring some order and systematics into the puzzling multitude of oxygen precipitate morphologies and secondary defects in order to enable the reader to make at least inspired guesses as to what kind of precipitate to expect at what temperature. a. T

< 550°C

Very few results from the literature exist for this temperature range as far as extended oxygen-related defects are concerned (Bergholz et al., 1985; Reiche, Reichel and Nitzsche, 1988). A large number of studies exist, on the other hand, on the subject of the formation of thermal donors, i.e., entities of 3 to 10 oxygen atoms (see, e.g., Ourmazd, Schroeter and Bourret, 1984, and references therein). Such studies have been, however, normally limited to comparatively short annealing times, below about 100 hours; for such times no detectable oxygen precipitates are formed. If, on the other hand, annealing times are prolonged to 500 hr to 5000 hr, not only does a sizable fraction of the oxygen disappear from solution, as monitored by IR (Fig. 7 shows an example), but several types of defects are found by TEM:

12.

527

GROWN-IN A N D PROCESS-INDUCED DEFECTS

Ribbonlike defects, which can be several micrometers in length (Fig. 8a). with a very small cross section of a few nm and crystalline structure (Fig. 8b); Stacking fault-like loop defects, most of which are associated with a ribbon defect (in fact, more than one ribbon defect can be attached to one loop; Fig. Ze is a high resolution image of a loop defect ) ; Defects that in a high-resolution image appear dark, that are unstable under an electron beam and that sometimes display an internal structure on { 1 1 1)-planes (Fig. 9). One self-consistent interpretation of these defects is that the ribbon defects are oxygen precipitates in a metastable crystalline structure (namely. coesite; Bourret et al., 1984). The loop defects and the dark bloblike defects are interpreted as agglomerates of self-interstitials, where the latter appear to be a prestage of the former. This defect identification is in quantitative agreement with the loss in dissolved oxygen, since the total volume of the ribbon defect is within the error limits (of about 3096) of what is to be expected if they contain the oxygen lost from solution. It is in order to mention that Bourret (1987) and Reiche et al. (1988) have, in the meantime, given an alternative interpretation. According to these authors, the ribbon defects are hexagonal Si, in which case the loop and blob defects have to be regarded as oxygen precipitates. Although this alternative defect identification cannot be ruled out completely at present. there are several difficulties: 0

0

Fig. 2d shows that the loop defects are extra (lI1}-planes, which implies problems in picruring the bonding arrangement of the oxygen atoms. The diffusion constant of oxygen is exceedingly low at this temperature. For such low diffusion coefficients, the ribbon shape is kinet-

*\

08061

0

300

GOO

900

Fic, 7 Rewiu,il oxygen concentmlion IOltr) -precipitates have formed in the bulk of the wafer (note the feature in the center of each etch figure marked by arrowheads; Heitzmann et al., 1994): (c) etch figure of a particularly large Nisiz precipitate with a flow pattern etch feature in its vicinity.

12.

GROWN-IN A N D PKOCESS-INDUCED DEFECTS

561

562

W . BERGHOLZ

FIG.30. (Continued).

12.

GROWN-IN A N D PROCESS-INDUCED DEFECTS

563

contamination of the wafer's back surface). By contrast, the interior of the wafer is haze free, instead the Ni has formed large precipitates in the bulk (Fig. 30b). The interpretation of this observation is simple. In the interior of the wafer there are efficient nucleation sites for the Niprecipitate nucleation o r sinks-sources for intrinsic defects in those regions of the wafer in which the !)-defects are normally detected. I t is remarkable that these defects are not stable above about 1000°C. since rapid annealing above this temperature prior to the decoration test destroys the effect. c'.

CZ-Mutc.riul

As already mentioned, the situation in CZ-material is complicated by the simultaneous oxygen precipitate formation and intrinsic defect aggregation during the cool-down from the melting temperature during the crystal growth process. The interaction between the two phenomena can be many: 0 0

0

Nucleation of oxygen precipitates on intrinsic defect clusters; Direct interaction of oxygen atoms with intrinsic point defects; Indirect interaction via a supersaturation of intrinsic defects; Indirect interaction via electrical effects (presumably marginal)

In spite of this complicated scenario, a few facts appear to be firmly established. Similar to FZ-material, A-defects are found in the outer perimeter of the wafer, provided the pulling speed of the wafer is in the range around 1 mmimin (Fig. 3 I . Fusegawa et al., 1991a). At the borderline to the interior of the wafer, there is a small region in which a high density of stacking faults develops during oxidation at, e.g., I000"C. (For standard device grade material. the pulling speed is usually chosen high

O D A

FIG. 31. Schematic distribution of etch pits on ii slowly pulled CZ-wafer: in the wafer perimeter shallow etch pits of A-defects are observed. whereas in the center a kind of flow pattern IS observed (compare to Fig. 37al.

564

W . BERGHOLZ

enough for the OSF ring to be outside those parts of the crystal ingot that are within the final wafer diameter). There are fewer A-defects in the wafer center, within the OSF circle. There is, however, another type of defect within the OSF circle that can be delineated by a novel technique (details in the following section). The similarity in the distribution of A-defects and the ring-shaped transition region for FZ and for CZ material is apparently quite remarkable and has led to conjecture that the defects in the wafer interior are, as for FZ Si, D-defects, a view that is not shared by all workers active in the field. Observations of the Si-material dependent gate oxide quality to be described in Section 3 further underline the similarities in the defect scenario in FZ- and in CZ-material. 3. GROWN-IN DEFECTS AND GATEOXIDE QUALITY a . G a t e Oxide Quality Dependence on the Starting Material

Among the most striking phenomena in device processing are the differences among different CZ-materials and the superiority of FZ- over CZ-material as far as gate oxide quality is concerned (Bergholz et al., 1989b). Figure 32 shows a comparison of the gate oxide quality for two CZ-materials in a voltage ramp test (Yamabe, Taniguchi and Matsushita, 1983). CZ-material has a significant fraction of fails of test capacitors at electric field strengths between 2 and 8 MVcm-'. By contrast. FZ-

50

50

kl n

ti

n

5

E

2

C

0 0

5

E I (MVlcm)

10

0 0

5 EI (MVlcm)

FIG.32. Voltage ramp test of the gate oxide integrity ((301) for CZ-materials from two different vendors. The difference in B-mode failure in the histogram of the electric field strength at which gate oxide breakdown occurs correlates with a defect density test in the bulk of the wafer as described in detail by Yamabe et al. (1983).

12.

565

GROWN-IN AND PROCESS-INDUCED DEFECTS

FZ with pretreatment

retreatment

" 8 9 'O 900I

ae

Y

>

JOt. 60

40

a.

I

A

C

P

E

F

FIG.3 3 . Gate oxide yield for 8 mm-' test capacitors in a two-stage constant current test (Bergholr et al.. 198%) for FZ-material from two vendors and four CZ-vendors. The circle5 denote the percentage of functional lest c,ipacitor\ after the first test stage 60 kA!crn-' for 100 nis. the 5quare\ after the second \tage 2 rnA lor 500 r n b .

material has a virtually 100% yield of intrinsic gate oxide failure (i.e., failure at an electric field strength around 10 MVcm-' (Fig. 3 3 ) . It is also noteworthy that the gate oxide quality of the epitaxial material is comparable to that of FZ-Si. 1). M o d e I: I n t c' rac.1ion o j Gro \\In -in Dqfic.1s un d M r t d ConI u rninii t ion

Based on a large body of experimental observations, a model to explain the differences in gate oxide quality between FZ- and CZ-Si has been put forward (Fig. 34, Bergholz et a l . . 1989b). The essence of the model that is schematically explained in Fig. 34 was that the gate oxide breakdown sites for B-mode failure are the surface near oxygen precipitates decorated by metal impurities. The essential point is that for a poor gate oxide quality. a high density of gate oxide breakdown sites, "enough" metal contamination must be present to "activate" the potential breakdown sites. A reasonable gate oxide quality i s thus possible even for a poor starting material with a high density of potential breakdown sites, if processing is carried out with little contamination or very efficient gettering.

566

W . BERGHOLZ

GROWN-IN I hqh

0

* METAL IMPURITY

DEFECT DENSITY I

n 0DEFECT

IW

-

I

I MDECORATO, DEFECT

FIG.34. Schematic representation of the Si-material dependent gate oxide degradation mechanism. The Si crystal contains defects that will be activated in the case of metal contamination-decoration. Therefore, reasonable gate oxide quality can be obtained for either low metal contamination or a low defect density. (The superiority of FZ-material is thus due to the low density of defects, i.e., potential gate oxide degradation sites.)

FZ-material, on the other hand, is more tolerant of metal contamination due to the low density of possible breakdown sites. In the light of new evidence on the defects in CZ-Si gathered in the last 1-2 years (to be described in detail in subsections c-e), the model is modified and put forward as the following hypothesis. Instead of an oxygen precipitate as the potential site for gate oxide failure, it is postulated that the potential breakdown site is initialized by an intrinsic defect agglomerate, the exact nature of which is yet to be determined. This model is at variance with an alternative explanation, namely, that the ultimate cause for the gate oxide weakness is a surface flaw generated, e.g., by an SC1-cleaning step. c. Correlution with the Crystal Pulling Speed Presumably the first step in the recent progress in establishing a correlation between defects in Si substrate and the gate oxide quality was the observation that for crystal pulling speeds below about 0.7 mm/min the gate oxide quality improves dramatically and is essentially comparable to that of FZ- or epi-material (Fig. 35, Tachimori, Sakon and Kaneko, 1990). Even more exciting is the observation that for an intermediate pulling

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GROWN-IN A N D PROCESS-INDUCED DEFECTS

567

speed most of the defective gate oxide test capacitors are located within the OSF-ring that occurs somewhere at an intermediate radius for pulling speeds around I mmimin (Fig. 36). Thus the gate oxide quality is good in the A-defect region and poor in the interior, in the case of FZ-material this would correspond to the region of the D-defects.

:I. Ctpeririicntcil L'i.idericc7f b r

Intrinsic Dt . . and Lagowski. J . (1982).J . Elecrrochrm. Sot. 129, 1638. Jasti-Leb\ki. L.. Soydan. R.. McGinn. J . . Kleppinger. R., Blurnenfeld. M., Gillespie. G . . Armour. N . . Goldsmith. B., Henry. W.. and Vecumbra. S. (1987). J . Elec.trcwhc~m. S w . 134. 1018. Vol. 3, S. P. Keller led.). de Kock. A . J . R. (1980). In Htrnclhocd ou .Sr/~trc~onduc~rors. p. 247. North-Holland, Amsterdam. de Kock. A . J . R.. Rocksnoer. P. J . . and Boonem. P. G . T . (1974). J . C 211. c7.s

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Kolbesen, B. 0. (1985). Summer School on Semiconductor Physics, Sao Paulo, Brazil. Kolbesen. B. O., Cerva, H., Gelsdorf, F., Zoth, G. and Bergholz. W. (1991). In Defects in Silicon 11, W. M. Bullis, U . Gosele and F. Shimura (eds.), p. 371. Electrochem. Soc., Pennington, N .J. Kolbesen, B. O., and Muehlbauer, A. (1982). Solid State Electron. 25, 759. Lascik. 2.. Booker, J. R., Bergholz. W.. and Falster, R. (1989). Appl. Phys. Lett. 55, 2625. Livingston, F. M., Messoloras, S . , Newman, R. C., Pike, B. C . , Stewart, R . J., Binns, M. J . , Brown, W. P., and Wilkes J. G. (1984). J . Phys. C: Solid St. Phys. 17, 6253. Marioton, B. P. R., and Gosele, U. (1988). J . Appl. Phys. 63, 4661. Matsumoto. S . , Ishihara, I., Kaneko, H., Harada. H., and Abe, T . (1985). Appl. Phys. Lett. 46, 957. Messoloras. S . , Schneider. J . R., Stewart, R. J., and Zulehner, W. (1989). Semicond. Sci. and Techno/. 4, 340. Nozaki, T . , Yatsurugi, Y ., Akiyama, N., Endo, Y ., and Makide, Y. ( 1974). J . Radioanal. C h e m . 19, 109. Ogushi, S . . Hourai, M . , and Shigematsu, T. (1992). MRS Spring Meeting. San Francisco, Abstract No. E1.4. Ourmazd, A., Schroeter, W., and Bourret, A. (1984). J . Appl. Phys. 56, 1670. Ourmazd, A., Taylor, 0. W., and Berk, J. (1987). Phys. R e v . L e f t . 59, 213. Patel, J. R . , Jackson, K. A,, and Reiss. H. (1977). J . Appl. Phys. 48, 5279. Petroff, P. W., and de Kock, A. J . R. (1975). J . Cryst. Growth 30, 117. Ponce. F. (1985). I n s t . Phys. Conf. Ser. 76, I. Reiche. M.,Reichel, J., and Nitzsche, W. (1988). Phys. Srat. Sol.(a) 107, 851. Rivaud. L..Anagnostopoulos, C. N . , and Erikson, G. R. (1988). J . Electrochem. Soc. 135, 437. Rocksnoer, P. J . , Bartels, W. J., and Bulle, C. W. T. (1976). J . Cryst. Growth 35, 245. Rocksnoer, P. J . , and van den Boom, M. M. B. (1981). J . Cryst. Growth 53, 563. Schomann. F., and Graff, K. (1989). J . Electrochern. Soc. 136, 2025. Secco d’Aragona, F. (1972). J . Electrochem. Soc. 119, 948. Seeger, A,. and Chik, K. P. (1968). Phys. Stat. Sol. 29, 455. Seibt. M. (1990). In Semiconductor Silicon 1990, H. R. Huff, K. J . Barraclough and J. Chikdwa (eds.), p. 663. Electrochem. SOC.,Pennington, N . J . Shimura, F.. Hockett, R. S. , Reed, D. A , , and Wayne, D. H. (1985). Appl. Phys. Lett. 47, 794. Swaroop, R.. Kim, N., Lin, W., Bullis, M., Shive, L., Rice, A ,, Castel, E . . and Christ, M. (1987). Solid State Technology (March), 85. Stavola, M.. Patel, J. R., Kimerling, L. C., and Freeland, P. E. (1983). Appl. Phys. Lett. 42, 73. Sumino, K., Harada, H., and Yonegawa, I . (1980). Jpn. J . Appl. Phys. 19, L49. Tachimori, H . , Sakon, T., and Kaneko, T. (1990). 7th Keitusho Kohgaku Syrnp. of Japan SOC.of Appl. Phys., JSAP Catalog No: AP 902217. Takeno. H.. Ushio, S. , and Tanekada, T. (1992). MRS Spring Meeting. San Francisco, Abstract No. E1.6. Tan, T. Y.. and Tice, L. K. (1976). Phil. M a g . 34, 615. Tan, T. Y Gosele, U . , and Morehead, F. F. (1983). Appl. Phys. A31, 97. Tanner, B. K. (1976). X-Ray Diffraction Topography. Pergamon Press, Oxford. Tempelhoff. K.. Spiegelberg, F., Gleichmann, R., and Wruck, D. (1979). Phys. Star. Sol.(a) 56, 213. Tiller, W. A., Hahn, S . , and Ponce, F. A. (1986). J . Appl. Phys. 59, 3255. .1

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Tsii. H . L. (1985). J . A p p l . P h n . 58. 377.5. Voronkov. V. V . (1982).J . C n . \ r . ~ ; t - o w r / i59, 625. van Werep. D. A . . Gregorkievicz. ‘I.. Hrkman H . H.. and Ammerlaan. C . A . J. (1986). M o f e r . Scieric c F o r u m . Vol. 10-12. p 1009 Trans Tech Publications Ltd.. Aederinannsdorf. Switzerland. Wright-Jenkins, M. (1977). J . Elec / r ( ~hcm. t . S ( J ( , . 124, 757. Yamabe. K.. Taniguchi. K . . and Mictw\hita. Y . (1983). In Defrcfs in Silicon. eds. W . M. Bull15 and L . C. Kimerling. p. 629. The Electrochern. S O C . , Pennington. N . J . Zulehner. W . ( 1989). In Srw7ic.e~r7dtr~ lor.\ . /wiptrrl/rc.s clnd Dyfc.c.r.5 in Grorrp / v Elernen/.$ t i n t / ///-V (‘ornponer7/.\. 0. Madelung and M . Schulz (eds.). p. 391. Landolt Boernstein Yew Series I I I ~ 2 2 b .Springer. Herliri

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SEMICONDU( I O K S A N D SEMIMETALS. VOL 42

C H A P T E R 13

Int rinsidhternal Get tering F . Shimura DEPARTMENT OF MATERIALS ScII;N('E SHIZUOKA INSTITUTE OF SCIENCE AND TECHNOLOGY, SHIZUOKA, JAPAN

I. 11.

INTRODUCTION

. . . . . .

SURFACE A N D INTERIOR

. . . . . . . . . . . . . MICRODEFECTS . . . . I . Surfuce Microdej~c.tc . . . . . . . . . 2. Interior Microde/iv.i.\ . . . . . . . . . 3. Summary of Proc-c~.~s-lndrct~rd Microdeferis

. . . .

. . . .

. . . .

. . . .

. . . . . . . . . . . . . . . . . I . General Remurk.\ . . . . . . . . . . . . . . 2. E/irninution oJ'u C'iinitrtnination Source . . . . . 3. fntrinsicllniernul Getrering . . . . . . . . . . 1v. O X Y G E N BEHAVIOR IN SII.I('ON . . . . . . . . . . . I . 0.rvgen 6fec.i on Silk o n Wqfer Properties . . . . 2. Oxygen Precipitution crnd Redissolution . . . . . 3. Oxygen Oui-Dijfi/.\ion and Denuded Zone Formation v. INlERNAL. GETTERING PROCESS A N D MECHANISM. . . . I , Thermul Cycle . . . . . . . . . . . . . . . . 2. Geirering Mechanism . . . . . . . . . . . . . 3. Geriering Sinks . . . . . . . . . . . . . . . VI. SUMMARY . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . .

111.

GETTERING

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. . . .

. . . . . . . .

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. . .

.

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577 579 5 80 583 590 593 593 596 596 599 599

599 606 610 610 61 I 612 614 615

1. Introduction

A modern VLSI/ULSI fabrication process includes hundreds of various steps. The process involves mainly subjecting polished Czochralski (CZ) silicon wafers to a variety of chemical, physical, and thermal treatments to fabricate active and passive device elements in the wafer surface region. Thermal oxidation and diffusion are usually performed at temperatures around 900°C or higher. Thus silicon wafers experience severe steps starting from the crystal growth through t h e complete device fabrication via wafer shaping processes. Even in recent high-quality silicon crystals, which are grown without any threading or observable dislocations. various kinds of microdefects are induced during thermal processes. Contamination, particularly with transition metals, during thermal processing initiates surface microdefects, while interior microdefects in

577 Copynght Q 1994 hy Acddemlc Press. Inc All rights of reproduction in any form reserved. ISBN 0-1?-752142-9

578

F. SHIMURA

CZ silicon wafers are caused exclusively by oxygen precipitation, which depends on various factors as discussed later in this chapter. Although there are many possible causes for device yield loss, the electronic device properties are greatly degraded by transition metals (e.g., Fe, Ni, Cu, Cr), when these impurities and the secondary defects are located in the device regions (Shimura, 1989) as extensively discussed in Chapters 12 and 14 in this volume. These elements are ubiquitous in a silicon processing environment, and unfortunately from the electronic device point of view, they have (i) extraordinary high diffusivity, (ii) low solubility and steep temperature dependence, and (iii) deep levels in the silicon forbidden band gap (Bergholz, et al., 1991). It is thus necessary to eliminate the detrimental effect of these impurities in order to ensure the high performance of electronic devices. In the fabrication of VLSI/ULSI devices, dry etching processes have been replacing wet etching processes in which silicon wafers are immersed in liquid etching reagents. Wet etching offers a low-cost, reliable, high-throughput process with excellent selectivity for the most processes; however, it is not capable of reproducible and controllable transfer of patterns in the micrometer or submicrometer range, which is required for VLSIKJLSI fabrication. Dry etching processes, which are based primarily on physical sputtering, ion-beam etching, or plasma etching, offer several advantages over the counterpart wet processes. However, dry processing has a tremendous contaminating capability and provides local heating and kinetic energy for contamination of the silicon wafer surface. Since reactive-ion etching (RIE) can selectively etch one chemical species in favor of another, it is possible to concentrate the residual species on the surface of the substrate, which is then driven into the circuit. i n particular, metallic impurities (e.g., Fe, Ni, Cu, Cr) can be sputtered from the chamber surfaces or components that consist of these elements and can then be deposited on the surfaces being etched. The intentional components of thin films (e.g., metal films or silicides) can also be the source of metallic contamination. Furthermore, reduced dimensions, particularly when a trench structure is used, are proving to be very difficult to clean, both from a particulate point of view and from a chemical solubility point of view, since the surface tension of the cleaning fluids is quite high in their pure states. Consequently, the contamination problem due to impurities has become more serious in the VLSI/ULSI era. The elimination of the effects of defects and impurities can be achieved through three steps: (i) suppression of the sources that may generate defects, (ii) annihilation of existing defects, and (iii) removal of impurities from the device regions in a silicon wafer. The process that accomplishes

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579

( i ) and ( i i i ) , particularly ( i i i ) in a narrow sense, is generally referred to as Krttrring. The term grftrring was originally used by Goetzberger and Shockley (1960)for the process of removing metallic impurities from the device region by a predeposited surface layer of either boron oxide or phosphorus pentoxide on a silicon wafer. Since metallic impurities are highly mobile, they diffuse from the surface of a wafer through the silicon lattice into the device regions very easily at processing temperatures. Gettering thus concerns mainly the removal of transition metals that diffuse quickly. cause surface microdefects (Shimura, Tsuya, and Kawamura, 1980a), and make lattice defects electrically active. The purpose of gettering is primarily to create a defect-free surface region in a silicon wafer used for electronic device fabrication. The gettering process involves three steps: ( i ) impurities are removed from the surface of a wafer, ( i i ) they then diffuse through the silicon lattice into certain gettering sinks at a position away from the device region, and ( i i i ) they are grttrred or captured by the gettering sinks. The gettering technology is one of the keys in the scheme of drjecr enginerring (Gatos, 1990; Rozgonyi, 1981; Rozgonyi, et al., 1987; Rozgonyi and Kola, 1990). 11. Surface and Interior Microdefects

Silicon microelectronic circuit devices are fabricated through various procesfes from the crystal growth through device formation processes. Figure 1 shows the steps for silicon device fabrication and the defects that can be induced into the silicon wafer. For convenience, these defects are classified into two categories: (i)grown-in defects and ( i i ) processinduced defects, which will be further classified into surface and interior defects. The major grown-in defects in high-quality silicon crystals for VLSliULSl are intrinsic point defects and impurities and their clusters. It should be emphasized that those defects listed in Fig. 1 may interact strongly with each other. Dislocations or stacking faults are not observed in the as-grown silicon crystals; however, their origin may inherently exist there and those lattice defects can be actualized by the subsequent thermal processes. In that case, the process-induced defects may more suitably be called process-grnrrated defects. Although process-induced defects are discussed in Chapter 12 in this volume. this section reviews briefly the surface and interior microdefects in terms of their origin and behavior, since it might be important to learn them for the understanding o f the gettering phenomenon which will be discussed in this chapter.

580

F. SHIMURA

I

I

Polvsilicon ’

I

impurities

I

6

I Crystal Growth 1

impurities point defects Grown-in Defects

. dopant striations oxygen donors microdefects -

dislocations

6 contamination Processes

mechanical damage

--.warpage

0 slip dislocation

I-}

Process-induced

surface microdefects stacking faults dislocations oxygen precipitates warpage

FIG.I . Semiconductor silicon manufacturing and device fabrication processes, and defects induced into silicon (Shimura, 1989; reprinted with the permission of Academic Press, Inc.).

I . SURFACE MICRODEFECTS a . General Remarks

Surface microdefects that manifest themselves as small saucer etch pits (S-pits) with a typical density of about 106/cm2are commonly generated in the surface of polished silicon wafers or epitaxial silicon films subjected to thermal oxidation at temperatures higher than 1100°C in a “not clean” furnace (Tsuya and Shimura, 1983). These surface microdefects have been attributed to contamination with transition metals during thermal processes (Pearce and McMahon, 1977; Shimura, et, al., 1980a). Figure 2 shows chemically etched figures of surface microdefects revealed by the Sirtl etchant for CZ silicon wafers subjected to different heat treatments in a “not clean” furnace. These figures indicate that ( i ) surface microdefects generated by wet 0, oxidation are larger in size than those generated by dry 0, oxidation, and (ii) these microdefects grow into large stacking faults by prolonged or repeated heat treatment at high temperatures. Moreover, it has been found that the density of

13.

IN1 KINbIC / I N T E R N A I GETTERINC

58 1

surface microdefects greatly depends on the cleanliness of the furnace used. b. Nutiire

The characterization by means of TEM and AEM suggests three different stages of surface microdefects that manifest themselves as S-pits by preferential chemical etching. but not as linear etch pits, which commonly correspond to stacking faults. The first stage is a tiny cluster of predominantly transition metals, which is so small that it does not show any visible contrast in the TEM image (Tsuya and Shimura, 1983). The second

F I G .2. Etched figures of surface defects delineated by Sirtl etching for ( 5 1 1 ) CZ silicon wafer3 subjected to different heat treatment (Shimura. 1989; reprinted with the permission 0 1 .Academic Press, Inc.).

582

F. SHIMURA

FIG.3. TEM micrograph of surface microstacking fault in CZ silicon subjected to heat treatment at I100"C for 2 hrs in wet O2 (Shimura, et al., 1980a).

stage is a small stacking fault with the impurity clusters at the central region of the fault plane as shown in Fig. 3 (Shimura, et al., 1980a). The stacking fault is extrinsic in nature and is bounded by a Frank partial dislocation loop, i.e., the same nature as a common OSF. The third stage is a small stacking fault whose Frank partial loop is heavily decorated with impurity clusters, often whiskers, as shown in Fig. 4 (Shimura, et al., 1980a). The impurities, which are located in the central region of the stacking fault and decorate the Frank loop, have been identified as copper or a copper-containing compound by STEM-EDX analysis (Shimura, et al., 1980a). Other transition metals such as Ni, Fe, Co, and Cr have also been observed to cause different types of surface microdefects (Stacy, Allison, and Wu, 1981).

c . Formation Mechanism The morphology of surface microdefects depends on the extent of contamination and on the nature of contaminants, as well as on the heat treatment conditions. A schematic model for the formation and growth of surface microdefects that result in the three different stages is shown in Fig. 5 (Shimura and Craven, 1984).Transition metals are supplied from the heat treatment environment and agglomerate in the surface region of

13. I N T R I N S I C / I N T E R N AGETTERING L

583

F I G . 3 . TEM micrograph of s u r f x e microstacking fault in CZ silicon subjected to heat treatment at I I(WC for 2 hrs in wet 0:. Frank partial dislocation loop IS decorated with whisker precipitates of Cu (Shirnura. et al.. 19XOa).

a wafer during a thermal process at a high temperature. At this stage, these agglomerates may cause elastic strain around them. but lattice defects such as stacking faults are not formed yet. After further agglomeration of impurities, with the resultant formation of larger clusters and proceeding oxidation. extrinsic stacking faults are generated at these sites as in the way of common OSF formation (Hu, 1974). If the contamination continues after the formation of stacking faults, the contaminants will be trapped preferentially at the Frank partial loop or decorate the stacking fault, resulting in stabilization of both the stacking faults and the contaminants themselves. By absorbing self-interstitials, these small stacking faults can grow into larger ones. which can be observed as linear etch pits by preferential chemical etching. 2.

~ N ERIOR I

DEFECTS

u . Origin

Thermally induced interior defects or bulk defects in CZ silicon crystals are primarily and most exclusively caused by oxygen precipitation. As

584

F. SHIMURA

transition metal contamination

I wafer

/

transition metal contaminant

e l 0

transition metal

luster

extrinsic-type stacking fault

O

transition metal decoration

/

1-7 FIG.5 . Schematic illustration showing formation and growth of surface microdefects in a silicon wafer (Shimura and Craven, 1984).

discussed in Chapter 2 in this volume, since oxygen is usually supersaturated in CZ silicon at modern processing temperatures, heat treatment leads to oxygen precipitation, which results in the formation of SiO, (x = 2 ) precipitates. Oxygen precipitates consists of amorphous or crystalline SiOz with a volume V,, per SiO, unit of roughly two times the atomic volume VSi in the silicon lattice. Accordingly, the precipitate growth can proceed either by relieving the excessive stresses by inducing plastic deformation of the silicon matrix, or by emitting one silicon selfinterstitial for every two oxygen atoms incorporated into the precipitate

13.

INTRINSI(./INTERNAI

GETTERING

585

in the surrounding silicon matrix (see Chapter 9 in this volume for details). The process of self-interstitial emission is, in principle, similar to the process that occurs during surface oxidation at the Si0,-Si interface (Hu, 1974). The main difference is that the overwhelming part of the volume expansion during SiO, formation due to surface oxidation is accommodated by viscoelastic flow toward the surface of t h e oxide film (Tan and Gosele, 1981), whereas such a process is not possible within a silicon crystal. As in the case of surface oxidation, self-interstitials generated by oxygen precipitates may condense into extrinsic-type dislocations or stacking faults. The straightforward correlation between oxygen precipitation and interior defect generation is made by referring to Figs. 6 and 7. The [Oil change shown in Fig. 7 was obtained for the same CZ silicon samples that indicated interior defects revealed by chemical etching shown in Fig. 6. It is quite obvious that a higher oxygen precipitation results in a higher density or larger volume of interior defects.

Fit, h la) Etched figures of internal defects delineated by Wright etching for I I I I ) CZ \iIicon octant samples subjected t o heat ti-eatmrnt for 64 hrs at temperatures shown: optical photograph of octants (Shimura. I W Y : Reprinted with the permission of Academic Press. Inc )

586

F. SHIMURA

FIG.6 ( b ) . Etched figures of internal defects delineated by Wright etching for (111) CZ silicon octant samples subjected to heat treatment for 64 hours at temperatures shown: optical micrographs of etch pits in each octant (Shimura, 1989: Reprinted with the permission of Academic Press, Inc.).

13.

INTRINSIC'/INTERNAL GETTERING

10

1 50 5:

587

w

as-grown

6

7

8

9

10 11 12

TEMPERATURE (x1Oo"C)

FIG 7 lntervtrtial oxygen concentrdtiim change in CZ silicon samples as a function of heat treatment temperature for 64 hr, in dry O? (Shimura and Tsuya. 1982a)

h. Natrrre The nature of interior defects depends primarily on the annealing temperature and heat-treatment sequence and has been extensively characterized by TEM (Bender, 1984; Bourret. Thibault-Desseaux and Seidman. 1984; Maher, Staudingher. and Patel, 1976; Matsushita, 1982; Ponce, Yamashita. and Hahn, 1983; Shimura, et al., 1980a; Shimura and Tsuya. 1982b; Tan and Tice. 1976). The first stage of thermally induced interior microdefects in CZ silicon is S O , precipitates, which are categorized into roughly three groups in terms of the precipitate morphology according to the precipitation temperature: ( i ) low-temperature range ( 1200°C) on as-grown silicon crystals has been proposed (Shimura, 1982), and it has been demonstrated that the effect of prior thermal history in the crystal puller can be erased to a large extent by a short-time heat treatment at 1320°C for silicon wafers (Fraundorf et al.. 1985).

606

F. SHIMURA

Precipitation

i

.

Partial , 100% precipitation Precipitation

i

INITIAL OXYGEN CONCENTRATION o oil^)

FIG.2 3 . Generic curve showing critical oxygen concentration [O,], and the relation between oxygen precipitation as a function of initial oxygen concentration [O,], (Shimura, 1991).

3. OXYGEN OUT-DIFFUSION A N D DENUDED ZONEFORMATION Generally a denuded zone (DZ) is defined as a surface depth zone where no interior defect is delineated, most commonly by a preferential chemical etching technique. Therefore the DZ does not necessarily mean a defect-free zone. Some interior defects can be observed with other techniques, such as TEM, that are more sensitive than the chemical etching or can be electrically detected even in the denuded zone (Rath et al., 1985). Strictly from the device operational point of view, a DZ should be defined as a wafer surface area that is free of electrically active defects as well as structural defects. For convenience in this chapter, however, a DZ is discussed as a wafer surface zone that is free of interior defects generated by oxygen precipitation. Accordingly a DZ can be formed by oxygen out-diffusion from the wafer surface, resulting in an oxygen-lean region, where the oxygen concentration is not high enough to generate oxygen precipitates (i.e., [O,] < [Oil,), since the critical radius dramatically increases with decreasing oxygen concentration. Such oxygen outdiffusion occurs in the wafer surface region during heat treatment in any ambient (Tice and Tan, 1981). The diffusion of oxygen in silicon is extensively discussed in Chapter 8 in this volume. Assuming that the thickness of the wafer is much larger than the corresponding length of oxygen out-diffusion and that there exist neither oxygen precipitates nor any traps for oxygen atoms, the concentration of

13.

I N I K I N W / I N T E R N A L GETTERING

607

oxygen atoms [O] (not necessarily be intcJrstitialoxygen atoms) at depth x from the surface for annealing temperature T for time t has been well given by the following error function (Ruiz and Pollack, 1978):

101( x , 1 )

=

101, + CIOI,,- [oI,~) erf(xi2W)

(2)

where [O],yis the solid soluhility of oxygen in silicon at T and [O], the initial oxygen concentration in the wafer. The [0],and D y are given by the Eqs. ( 3 ) and (4).respectively (Mikkelsen, 1986):

[O], = 9 x 10" exp( - I .S2/kT) (atoms/cm3).

(3)

D'f'

(4)

=

0.13 exp( - 2.53ikT) (cm?/sec).

in the The oxygen concentration at the SiOz/Si interface reaches case of annealing in an oxygen ambient, and oxygen out-diffuse to the interface where the oxygen may help SiOz growth, while the oxygen concentration at the wafer surface reaches zero in an inert ambient. The out-diffusion of oxygen for both cases is depicted in Fig. 24, where l O~ ~ S. ~l ~, and ~ ~ I0,1,,s,,,2 ) ~ , ~ are the equilibrium concentra[O,,ls, [ O , . ] S ~ O OXYGEN

INERT AMBIENT

I

,

:sll

FIG 24 Schematic illustration rhowing oxygen outdiffuwm (a) in oxygen ambient, and cb) in inert gds ambient (Tice and T . i n , 1981)

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F. SHIMURA

100WC/64h

>

3

0

10

20

30

DEPTH (pn)

115WCi2h

40

DEPTH (pm)

DEPTH (pm)

FIG.25. Calculated depth profiles of oxygen concentration for silicon wafers with [O,],, of 10. 15, and 20 ppma: (a) (7SOoC/64 hr/02) heat treatment, (b) (100O0C/64 hr/O,) heat treatment, and (c) (11SO0C/2 hr/02) heat treatment (Shimura, 1989; reprinted with the permission of Academic Press, Inc.).

tion of oxygen in Si, in SiO, at the SiO,/Si interface, in SiO, at the ambient-SiO, interface, and in ambient at the ambient-SiO, interface, respectively (Tice and Tan, 1981). Thus, strictly speaking, [O], in Eq. (2) should be replaced with [O,],, and zero for heat treatment in oxygen and inert ambients, respectively. Figure 25 shows the depth profiles of oxygen concentration calculated using Eqs. (2)-(4) in three different heat-treatment cases for silicon wafers with three different [O,], values. Assuming a certain critical oxygen concentration [O,], (e.g., 14 ppma) for the occurrence of oxygen precipitation, the denuded zone depth depending both on [O,], and annealing conditions are obtained as depicted in Fig. 25. Oxygen precipitation occurs in the wafer region deeper than the denuded zone-in other words, in the region whose [Oil is higher than [O,],. It is obvious that the W,, is infinite or equal to the wafer thickness in silicon wafers whose [O,], is less than [O,], (see the case with [O,], = 10 ppma shown in Figs. 25 and 16 (a)). In addition, in the case that the [O,], is extremely high or the diffusion of oxygen is negligibly small, the W,, is nearly zero as shown in Fig. 16(c) and 25(a). It is noteworthy that, in principle, denuded zones are symmetrically formed in both the front and back surfaces of a silicon wafer, and internal defects as IG sinks also distribute symmetrically in the wafer bulk region. Accordingly, in principle an IG treatment will not cause wafer warping or bowing, which can be a serious problem in device patterning, as most EG treatments do. It should be emphasized that, as depicted in Fig. 23, a critical concentration [0,1, may vary with various heterogeneous oxygen precipitation

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INTKINSI(./INTERNAL GETTERING

609

factors. Moreover, the diffusivity of interstitial oxygen D F can be influenced by the presence of point defects (Heck, Tressler, and Monkowski, 1983; Gosele and Tan, 1985). subsidiary light impurities such as carbon (Shimura, Higuchi, and Hockett, 1988) and hydrogen (Fuller and Logan, 1957; Newman, 1991 ; Zhong and Shimura. 1993), metallic impurities (Newman, Tipping, and Tucker. 1985), and dopant species (Gass et al., 1980). For example, the effect of carbon on oxygen out-diffusion is shown in the following. The out-diffusion behavior of oxygen and carbon in CZ silicon wafers with and without carbon doping ([C,] = 6 ppma) was investigated by SIMS, and the experimental results were compared with the counterpart ones calculated using the diffusion coefficient in literature (Mikkelsen, 1986; Newman and Wakerfield. 1961). The results showed that oxygen diffusion is greatly retarded by oxygen precipitation in both the cases of carbon-doped and undoped silicon and strongly support a vacancydominant diffusion mechanism for oxygen in silicon (Heck et al., 1983). In Fig. 26(a), it is found that the diffusion of both oxygen and carbon is significantly enhanced in carbon-doped silicon subjected to heat treatment at 750°C. Moreover, it should be noted that the obtained diffusion constants of oxygen and carbon are in good agreement (Shimura, 1991). This result was attributed to the formation of fast-diffusing 0-C complexes, i.e., perturbed C(3) centers that consist of a few oxygen atoms per carbon atom (Shimura. Baiardo, and Fraundorf, 1985; Shimura,

(a)

EiQoW

(b) 1 Q M O U 6 4 . h

FIG. 26. SIMS and calculated depth profiles of oxygen and carbon concentrations in carbon-doped DZ silicon subjected to different heat treatments (Shimura et al.. 1988; Shimura. 19911.

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F. SHIMURA

1986). This is similar to the fast-diffusing gaslike molecular oxygen in silicon proposed by Gosele and Tan (1982). On the other hand, the diffusion of both oxygen and carbon is significantly retarded at 1000°C as shown in Fig. 26(b). The retardation of both oxygen and carbon diffusion has been primarily attributed to the oxygen precipitation that results in dense self-interstitials and the formation of slow-diffusing complexes such as Si-0-C (Shimura et al., 1988). Consequently, as summarized in Figs. 18 and 23, the DZ width in silicon wafers depends on (i) initial oxygen concentration ([O,],), (ii) heat treatment conditions ( T , r ), (iii) critical oxygen concentration ([O,],), and (iv) oxygen diffusivity (DF). The [O,], and DF greatly depend on heterogeneous factors in addition to [O,], and ( T , t ) . V. Internal Gettering Process and Mechanism

I . THERMAL CYCLE

For the purpose of forming an optimum denuded zone and interior defects, several thermal cycles for IG have been proposed (Kishino et al., 1984; Nagasawa, Matsushita, and Kishino, 1980; Peibt and Raidt, 1981; Tsuya, Ogawa, and Shimura, 1981). The IG thermal cycle commonly used is called a high-low-high (or-medium) sequence, which in principle consists of the following three steps: 1. Oxygen outdiffusion heat treatment at a high temperature (>I IOOOC) for DZ formation. In order to prevent OSF generation, this heat treatment is usually carried out in an inert ambient. 2 . Heterogeneous SiO, nucleation site formation at a low temperature (600-750°C). Since preannealing at a high temperature suppresses oxygen precipitation during the subsequent heat treatment, annealing at a low temperature is required to grow SiO, embryos. 3 . Gettering-sink introduction at a medium or high temperature (1000-1 100°C). During this heat treatment, SiO, precipitates grow larger and lattice defects as IG sinks are induced in the region under the denuded zone.

Furthermore, a multistep heat treatment consisting of several steps at temperatures from low (-500°C) to high (-1150°C) has proved its effectiveness on IG in low [O,], or heavily doped n + silicon wafers where oxygen precipitation rarely occurs (Tsuya, Ogawa and Shimura, 1981). However, in general, IG heat treatment requires a long period of furnace operation in addition to the time for device fabrication processes. This time-consuming heat treatment is a major disadvantage of an 1G tech-

13.

I N T H I N W / I N T E R N A L GETTERING

611

nique. In order to utilize 1G in practical device processing, silicon wafers must be treated so that inrrirrsic, gettering occurs simultaneously during devicc processes without any additional IG heat treatment.

3.

GE-TTERING

MECHANISM

The fundamental understanding of gettering mechanism has been well described in recent reviews by Weber and Gilles (1990) and Tan (1991). In principle, all metallic impurities dissolve in the silicon lattice both on interstitial and substitutional sites, i.e.. M , and M , , respectively (Tan, 1991). Because of t h e smaller diffusivity of M , under practical thermal conditions. M , is more difficult to getter than M I . Fortunately, the most prominent metallic contaminants (e.g., Cu, N i , and Fe) dissolve in silicon predominantly as M I . ,4 mechanism for IG is qualitatively illustrated in Fig. 27 in terms of diffusion of metallic impurities into the bulk region of a silicon wafer which is subjected to thermal treatment (Weber and Gilles, 1990). In the figure the concentration of M , is presented as function of wafer depth (x/ W L I L )for three stages. When metallic contarninants are introduced onto the wafer surface, the metal atoms will diffuse rapidly into the bulk region in order to establish an equilibrium concentration (C,,) at a processing temperature (T,,; usually at 850°C or higher), Fig. 27(a). Upon lowering the temperature to T , , the metallic impurities become supersaturated since the concentration exceed4 the solid solubility ( C , ) at T , , and they precipitate very rapidly in the interior region. The precipitation should occur preferentially at internal defects in gettering region since crystalline defects can provide low-energy heterogeneous nucleation sites. This is the reason to call such internal defects IG sinks. While in the denuded Lone. the precipitation is much more difficult since homogeneous nucleation, which requires high energy and high supersaturation, can be only the process of precipitation. This stage is depicted in Fig. 27(b). Once the metallic impurities precipitated in the bulk region, the impurities in the DZ may diffuse rapidly into the bulk region by a driving force due to the concentration gradient generated between the two regions as shown in Fig. 27(c). The metallic impurities may diffuse toward defects and segregate preferentially in the defect region even when they are not supersaturated at a high temperature. Thus, no metal precipitation or segregation occurs in the DZ, while metallic impurities precipitate or segregate in the internal defect region of a silicon wafer. The diffusion process in the denuded zone can be characterized by a parameter 0 = D y / WbZ where I)" is the diffusion coefficient of metallic impurity. M . According to t h e model shown in Fig. 27 (Weber and Gilles,

612

F. SHIMURA

1.0

1

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0.0

n

.

CO

0.8

0.4

1.2

1.6

. . I

L

0

0.0

0.8

0.4

1.6

1.2

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,

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FIG.27. Change in the metallic impurity concentration in denuded zone and bulk region of silicon wafer showing a model of internal gettering (Weber and Gilles, 1990; reprinted with the permission of The Electrochemical Society, Inc.).

1990), the gettering temperature and time for a given impurity species and concentration level can be optimized. If there is a sufficient capability of IG sinks for impurity precipitation, the gettering process can be uniquely determined by D', W,,, and the cooling rate or temperature. The concentration of M drops to 10% of its initial value when 0 becomes 1. It should be noted that the gettering of metallic impurities, such as Cu and Ni, that have the significantly larger solubility starts at considerably lower temperatures than that for others, such as Fe, Cr, Co, and Mn. It might be needless to say that a longer gettering time is required for slow-diffusing impurities such as Ti and M , . 3. GETTERING SINKS

It has been recognized that internal defects can be effective IG sinks. As to the question of the dominant gettering sites, however, several dif-

13.

INI HINSIC/INTEKNAI.

613

CETTERING

ferent models have been proposed until now as depicted in Fig. 28 (Shimura, 1989). It has been observed that low densities of dislocations or stacking faults are effective gettering sinks for Cu-related surface microdefect, but dense microprecipitates of SiO, are not (Shimura et al., 1981; Tsuya and Shimura. 1983). Accordingly, it has been proposed that dislocations or stacking faults are required for effective 1G sinks (Shimura et al., 1981; Tan et al.. 1977). It has been also reported that the density of stacking faults correlated well with gettering efficiencies (Graff, Hefner, and Hennerici, 1988). The effect of these lattice defects on gettering impurities is explained primarily by the Cottrell effect. in which solubility of a foreign atom will be greater in the vicinity of a dislocation (Nabbaro, 1967). Moreover, dangling bonds introduced by edge dislocations or stacking faults have been considered to be closely spaced acceptors since a dangling bond has an unpaired electron (Read. 1954). Therefore, dislocations may directly attract negatively charged species. Oxygen precipitates themselves have been considered effective gettering sinks for Ni and Fe atoms. Using high-resolution TEM, Ourmazd and Schroter (1984) detected Ni precipitates, Nisi?, near oxygen precipitates that show neither dislocation nor stacking faults. Accordingly, the formation of Nisiz near oxygen precipitates, namely, the gettering of Ni. was explained on the basis of the emission of silicon self-interstitials from the oxygen precipitates that condense with Ni to form a silicide (Ourrnazd and Schriiter, 1984). Moreover oxygen precipitates without any association of self-interstitials can he effective heterogeneous nucleation sites Contaminants

0

P

0

* *;* * .** *

v

* * *

Strain field

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Si-0 precipitates

Oxy. ppt-induced lattice defects

.i;.i A‘

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h

a

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f 16 ZX Schematic illustration 5hon ing possihle sinks for internal getterinp (Shirnura. 1989. reprinted with the permission ot Academic Press, Inc.).

614

F . SHIMURA

for metallic impurities by forming a new phase directly connected to a redissolution of oxygen precipitate (Colas and Weber, 1986; Gilles, Weber, and Hahn, 1990; Weber and Gilles, 1990). In addition, more strikingly, the denuded-zone formation and internal gettering in oxygen-free FZ silicon wafers have been reported as well (Nauka et al., 1985b). Eventually the process has been explained by the out-diffusion and precipitation of silicon self-interstitials, instead of oxygen, which can act as gettering sites for metallic impurities (Nauka et al., 1986).It has been identified by analytical TEM observation that internally gettered centers are three-dimensional butterfly-shaped complexes consisting of multiply extended dislocation loops and a high density of microprecipitates, which are mostly Cu-, occasionally Ni-, and very rarely Fe-silicides (Ueda et al., 1986). Moreover, an IG phenomenon has been found in oxygen-Iean MCZ silicon wafers where oxygen precipitates are rarely found, and there is a mechanism by which metallic impurities can be gettered by combining with interstitially dissolved oxygen atoms (Futagami et al., 1986). Consequently, all the internal defects, including oxygen atoms, depicted in Fig. 28 can be effective gettering sinks for specific impurity atoms depending on their physical and chemical properties. VI. Summary

The IG process is clean in principle and can provide effective gettering sinks in the region close to the surface where electronic devices are fabricated. These schemes of IG are more favorable than the counterpart EG techniques to the VLSI/ULSI technology. However, IG requires the strict control of various oxygen-related processes in order to perform uniform and consistent gettering. For this goal, the silicon wafers used for the device fabrication must satisfy the following major requirements: ( I ) they must have a specific [O,], with uniform radical distribution across the wafer diameter, and (2) they must result in a uniform and reproducible A LO,], DZ, and interior defects. The control of oxygen incorporation into growing silicon crystals has been well established as discussed extensively in Chapter 2 in this volume; however, oxygen precipitation and resulting interior defects have not necessarily been controlled well at this moment, since they are greatly influenced by various factors that are not easy to control. Moreover, additional thermal cycles required for IG are not desired from the device fabrication cost point of view. Therefore silicon wafers and the device fabrication sequence must be designed so that the IG effect can be expected in the processed wafers during ordinary device processes without any additional IG thermal cycle.

13.

INTRINSIC /INTERNAL GETTERINC

615

In order to eliminate the cumbersome oxygen-related phenomena including mechanical problems and 1G thermal cycles, an approach that uses silicon wafers with [O, I,, far below [O,], might be viable if an alternative gettering technique will remain effective throughout entire device fabrication processes or if the entire process is clean enough to require no gettering technique. Finally, i t is emphasized that ( i ) the device zone must be free of unwanted impurities, structural imperfections, and wafer strain, i.e., a real defect-jroe zone instead of a conventional denuded zone must be prepared by gettering or other treatment, and ( i i ) the primary effort undertaken to eliminate the detrimental effect of contamination is to remove the sources. but not to getter them.

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Kaiser, W. (1957). Phys. Rev. 105, 1751. Kishino, S.,Aoshima, T., Yoshinaka, A., Shimizu, H . , and Ono, M. (1984). Japan. J . Appl. Phvs. 23, L9. Maher, D. M., Staudinger, A., and Patel, J. (1976). J . Appl. Phys. 47, 3813. Matsushita, Y. (1982). J . Crystal Growth 56, 516. Mikkelsen, J. C., Jr. (1986). In Oxygen, Carbon, Hydrogen and Nitrogen in Crystalline Silicon, J . C. Mikkelsen, Jr., S. J. Pearton, J . W. Corbett, and S. J . Pennycook (eds.), p. 19. Materials Research Society, Pittsburgh. Nabaro, F. R. N. (1967). Theory of Crystal Dislocations. Oxford University Press, Oxford. Nagasawa. K . , Matsushita, Y., and Kishino, S. (1980). Appl. Phys. Lett. 37, 622. Nauka, K.,Lagowski, J., and Gatos, H . C. (1985a). In Impurity Diffusion and Gertering in Silicon, R. B. Fair, C. W. Pearce, and J . Washburn (eds.), p. 175. Materials Research Society, Pittsburgh. Nauka, K.. Lagowski, J., Gatos, H. C., and Li, C . J. (3985b). Appl. Phys. Lett. 46, 673. Nauka. K.. Lagowski, J., Gatos. H. C., and Ueda, 0. (1986). J . Appl. Phys. 60, 615. Newman, R. C. (1991). In Defects in Silicon I I . W. M. Bullis, U. Gosele, and F. Shimura (eds.). p. 271. The Electrochemical Society, Pennington, N.J. Newman, R.C., Tipping, A. K., and Tucker, J. H. (1985). J . Phys. C; Solid State Phys. 18, L861. Newman, R. C., and Wakerfield, J. (1961). J . Phys. Chem. Solids 19, 230. Ogino, M., Usami, T., Watanabe, M., Sekine, H., and Kawaguchi, T. (1983). J.Electroc.hem. Soc. 130, 1397. Ohmi, T. (1991). In Defects in Silicon I I , W. M. Bullis, U . Gosele, and F. Shimura (eds.), p. 351. The Electrochemical Society, Pennington, N.J. Osaka, J.. tnoue, N., and Wada, K. (1980). Appl. Phys. Lett. 36, 288. Ourmazd. A.. and Schroter, W. (1984). Appl. Phys. Lett. 30, 781. Pearce, C. W . , and McMahon, R. G. (1977). 1. Vac. Sci. Techno/. 14,40. Peibt, H.,and Raidt, H. (1981). Phys. Stat. Sol. A68, 253. Ponce. F. A.. Yarnashita, T., and Hahn, S. (1983). Appl. Phys. Lett. 43, 1051. Rath, H. J . , Reffle, J., Huber, D., and Eichinger, P. (1985). In Impurity Diffusion and Gefferingin Silicon, R. B. Fair, C. W. Pearce, and J. Washburn (eds.), p. 193. Materials Research Society, Pittsburgh. Read, W. T., Jr. (1954). Philos. Mag. 45, 775. Robinson, P. H., and Heirnan, F. P. (1971). J . Electrochem. Soc. 118, 141. Rozgonyi, G. A. (1981). In Semiconductor Silicon 1981, H . R. Huff, R. J. Kriegler, and Y. Takeishi (eds.), p. 477. The Electrochemical Society, Pennington, N.J. Rozgonyi, G. A., Deysher, R. P., and Pearce, C. W. (1976). J . Electrochem. Soc. 123, 1910. Rozgonyi, G. A., and Kola, R . R. (1990). In Defect Control in Silicon, K. Sumino (ed.), p. 579. North-Holland, Amsterdam. Rozgonyi, G. A., Salih, A. S. M., Radzirnski, Z., Kola, R. R., Honeycutt, J . , Bean, K. E . , and Lindberg, K. (1987). J . Crystal Growth 85, 300. Ruitz. H. J . , and Pollack, G . P. (1978). J . Electrochem. Soc. 125, 128. Salih, A. S. M., Kim, H . J., Davis, R. F., and Rozgonyi, G. A. (1984). In Semiconductor Processing, D. C . Gupta (ed.), p. 272. Am. SOC.Test. Mater., Philadelphia. Shimura, F. (1981a). Appl. Phys. Lett. 39, 987. Shimura, F. (1981b). J . Crystal Growth 54, 588. Shimura, F.(1982). In VLSIScience and Technologyil982, C . J. Dell’Ocaand W. M. Bullis (eds.), p. 17. The Electrochemical Society, Pennington, N.J. Shimura, F. 11986). J . Appl. Phys. 59, 3251.

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Shirnura. F. (1989). ,Sc.mic.orzduct o r Silicon Cr\.,tcrl Technologv. Academic Press. San Diego. Shiniura. F. ( I991 ). Solid Siore Plit,nomtwti 19-20, I , Shiniura. F.. Baiardo. J . P.. and Fraiindorf. P. (1985). Appl. Phvs. Lerr. 46,941. Shirnura. F. and Craven. K. A. 119x4). In The Plrv5ic.s of' VLSI. J . C. Knight (ed.). p. 205. American Institute of Physics. New York. Shiniura. F.. Higuchi. T.. and Hochett. K. S. (1988). Appl. P h v s . Lert. 53, 69. Shimura. F.. and Tsuya. H. (1982a).J . Elcc./roc.lrem. Sex. 129, 1062. Shimura. F.. and Tsuya, H. (1982h). J . E l t ~ c ~ r r c x h e r nSoc. . 129, 2089. Shimura. F.. Tsuya. H.. and Kawmiura. T. (198Oa).J . Appl. Plivs. 51, 269. Shiniura. F.. Tsuya. H.. and Kaw;iniui-a. 7 .( IYXOb). Appl. Phys. Lett. 37, 483. Shiniura. F . . Tsuya. H . . and Kawaniurii. T. (1981). J . Electrochem. Soc. 128. 1579. Shirai. H . . Yamaguchi, A . . and Shiniui-a, I-' (1989). Appl. Ph?s. Lett. 54, 1748. Stacy. W . IT. Allison. 0. F., and W u . I' C . (1981). In Scmic,onduclor Silicwn l Y 8 l . H . R. Huff, R. J . Kriegler, and Y. I;ikei\hi ( e d \ . ) . p. 344. The Electrochemical Society. Penninpton. N . J . Takano. Y.. Koruka. H.. Ogirima. M.. and Maki. M. (1981). In Srrniconduc.tor .Silicon I Y X I . H . K . Huff, R . J . Kriegler. and Y. Takeishi (eds.). p. 743. The Electrochemical Society. Pennington. N.J. 'lamura. M.. Isomae. S . . Ando. T . . Ohvu, K . . Yamagishi. H . . and Hashimoto. A. (1991). In Dc~fc~.r.r in ,Sili(,on I / . W . M. Bullis. U . Gosele. and F. Shimura (eds.). p. 3. The Electrochemical Society. Pennington. N .J. Tan. T. Y. (1991). In fIqf&.is in .Silt[ o r i / I . W . M . Bullis. U . GZisele. and F. Shimura (eds.). p. 613. 'The Electrochemical Societv. Pennington. N . J . 'Tan. 7 . Y.. Gardner. E. E . . and 'Iice, W . K. (1977). Appl. Phv.5. Lrri. 30, 175. Tan. T. Y .. and G6cele. C . ( 1981) A p p l . Phv.r Letr. 39, 86. Tan. T-.Y.. and Tice. W . K. (1976) / ' / i ~ / o s . Mtrp. 34, 615. 'rice. W . K.. and Tan. T . Y. 11981 ) . In / k ~ c r . in s Srrnicondrrcrors. J . Narayan and T. Y. Tan (eds.). p. 367. North-Hollmd. Amsterdam. l s u y a . H . . Ogawa. K.. and Shimui-a. f:. (1981). Jupari. J . Appl. Phys. 20, L31. Tsuva. H . . and Shiniura. F. (19x3) P/rv,$.S k i r . Sol ((1) 79, 199. Tsuva. H.. Shimura. F.. Ogawa. K . . ond Kawamura. T. (1982). J . Eleelrochem. S o c . 129, 374. t!eJa. 0 . .Nauka. K.. Lagowshi. J . . and (Jato\,. H . C. (1986). J . Appl. Phys. 60. 6 2 . I J w m i . T.. Matsushita. Y.. and Opino. M . (19x4). J . Crvsrul GroM.tli 70, 319. Wada. K.. Inoue. N.. and Kohra. K . (1980). J . Cnjstcil GroM.tli 49, 749. Weher. E. K..and Gilles, I). (1990). I n Srnrr~.ondirrrf)rSilicon lY90. H. R. Huff. K . G . Barraclough. and J . Chikawa (ed\ ). p. 5 8 5 . The Electrochemical Society. Pennington. N.J. Yasutake. K.. IJmeno. M.. and Kamahe. H. (1984). Phys. Slut. Sol. ( ( I ) 83, 207. Zhong. I,.. and Shimura. F. (1993) J . A p p l . P h \ . 73. 707.

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Oxygen Effect on Electronic Device Performance H. Tsuyu RESEARCH A N D D F V E l O P M E N I CZROLIP N E C CORPORATION S A G A M I H A R A , JAPAh.

I. 11.

INTRODUCTION

. . . . . . . . . . . . . . . . . . .

619

DEFECTS . . . . . .

62 I 622 623 625 625 628 630 633

D E V I C E CHARACTERIS.II('S A N D C R Y S T A L

I . Device

Structure

L ~ J C'rvstcrllinr .

Defec./.s . . . . . . .

2 . Failure Modes in 1.SI Devic,es . . . . . . . . . . . 111.

DEFECT GENERATION . . . . . . . . . . . . . . . . I . O.rvgen Precipitctre Rcltited Fuilure Modes . . . . . .

2 . Residuul Stress of' S i 0 2 Film . . . . . . . . 3 . O.rygen Related 1kfi.c.t.s by I o n lmpluntarion . 4. O.ride Film Degrudution . . . . . . . . . 5 . Lattice Defect Gc,nercrtion Due t o Heuvv Mettrl Con tamination . . . . . . . . . . . . I V . IMPROVEMENT OF D E V I CYIEL.D E . . . . . . . . I . Intrinsic Gettering App/ic.ct/ion t o VLSI . . . 2 . Homogenization (it Prcc.ipituted Oxygen . . .

. . . .

. . . . . . . . . . . . . . . .

. . . .

. . . . Epitaxial Wcifers t o

3 . Intrinsic. G'e'tteritiX App/ic.ci/icm0.f VLSl . . . . . . . . . . . . . . . . 4. Gettrruhi1itvf;ir t l e c r ~ ~Meter1 v lrnpurities . . 5 . Control of Mec~htinii~~il .StrcnXth . . . . . 6 . Advonced Intrinsic- Gcrtcring . . . . . . . V. S U M M A R Y . .. . . . . . . . . . . . . . . A ~ ~ k n o ~ ~ ~ l e d ~ m.e n. r s. . . . . . . . . References

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634 635 636 640 647 65 I 652 660 663 663 664

I . Introduction ULSI, as seen symbolically in the development of D R A M size reduction and higher-degree integration. has made great progress. For example, D R A M is now commercially going into the era of 16 Mbit passing through 4 M . I n parallel with the development of high-performance devices, it is not too much to say that silicon device industry is characterized by constant struggles with chip yield. Factors affecting chip yield are grown-in crystal defects. particulate, residual ions and so on as well as process-induced failure modes. Furthermore. the unwanted heavy metal impurities in619 Copyright 9 1994 hy Academic Press. Inc All right\ of reproduction In any form reserved. ISBN 0-1?-75?14?-9

620

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duced by the chip fabrication process degrade the electrical characteristics resulting in the decrease of chip yield. Oxygen atoms are closely related to electronic device performance. If crystalline defects induced by oxygen precipitation exist near device active regions, they degrade device characteristics. On the other hand, as described in Chapter 13, inner defects due to oxygen precipitation play a role of gettering sinks for heavy metal impurities, resulting in good device yield. Furthermore, as discussed in Chapter 1 1 , oxygen atoms prevent the dislocation movement, giving rise to good mechanical strength, however, excessive oxygen precipitates have the possibility of degrading the mechanical strength of a wafer. For this reason it is said that oxygen atoms are “two-edged swords” for device performance. Historically, in order to achieve a high-performance device, new process technologies and new device structures have been developed and introduced into mass production. For example, ion implantation and dry etching technologies have been utilized from the era of 4K DRAM and 16K DRAM, respectively. As for device structures, LOCOS isolation has been adopted since the era of 1-4 K DRAM, and trench capacitor and LDD structures have been practically introduced into 1M DRAM production. Figure 1 illustrates the trend of new technologies and DRAM high integration (Tsuya, 1991a). Though these new technologies realized high10

3 1.20.5

0.1

Process __

DRY ETCHING ) w

1960

,

,

,

1970

1980

1990

2’ I0

YEARS

Fic. I . Trend of DRAM high integration and related technologies (Tsuya, 1991a).

14.

OXYGEN EFFFC 1 O N I-I F C r R O N l C DEVICE PERFORMANCE

621

100 1G 256M64M 16M

0.01

0.1

4M

1M

1

10

DEFECT DENSITY (cm-’) k i ~ 2 Calculated curve of LSI chip vield v \ the equivalent detect density tor each generation of DRAM ( r s u y d . 1991t r )

performance devices, at the same time they introduced t h e unwanted heavy metal impurities and increasing local stress in the device region. Heavy metal impurities easily gather around these local stresses, resulting in the increase of leakage current. In order to fabricate VLSl devices with high yield, it is fundamentally important to suppress crystallographic microdefects and completely eliminate heavy metal contaminants in device active regions. These microdefects originate from bulk defects such as oxygen precipitates and dislocation or heavy metal contamination during device processing. In this chapter the oxygen effect on electronic device performance will he discussed from the standpoint of device characteristics and yield improvement. 11. Device Characteristics and Crystal Defects

Figure 2 shows the curve of LSI chip yield versus the equivalent defect density due to crystalline defects. particulate. residue of resist and so on for each generation of DRAM calculated (Tsuya, 1991b), using the forand u are yield, the mean defect mula of Y = exp( -Dou), where Y. D,, density and the susceptible area of a device, respectively (Murphy, 1964). I n order to obtain good chip yield, the equivalent defect density must he dramatically suppressed with increased packing density, because 61 increases with increased packing density. One of the severe criteria of DRAM is leakage current. Acceptable leakage current roughly estimated using the formula of I , = 0 . where I , , Q, and 1, are leakage current. capacitance and refresh time. respectively, must be drastically re-

622

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I

I

4M

16M

TSUYA

64M

I

I

256M

1G

PACKING DENSITY OF D R A M

FIG.3 . Acceptable leakage current per unit cell at 25°C vs. packing density of DRAM (Tsuya. 1992).

duced with increasing packing density as shown in Fig. 3 (Tsuya, 1992). For example, the leakage current per unit cell of 256M DRAM must be less than A at 25°C. It has been pointed out that heavy metal impurities and crystalline defects are related to leakage current. I . DEVICE STRUCTURE vs. CRYSTALLINE DEFECTS

Basically, there are two kinds of device structures, MOS (metal oxide semiconductor) and bipolar types. In the case of the MOS transistor, majority carriers from a source are controlled by the electric field on the silicon surface applied by gate electrodes. Majority carriers passing through channel are drift currents, and they are proportional to the voltage of gate electrode; that is, the action of the MOS transistor is influenced by its crystal surface. On the other hand, for the bipolar transistor, minority carriers injected into base region from the emitter are collected into a collector region by the concentration gradient of carriers through the base region. Minority carriers are diffusion currents, and they move into the interior of a crystal unlike the MOS transistor. The amplification potential of a bipolar transistor is strongly influenced by the injection efficiency of minority carriers from emitter to base and their lifetime in the base region. These phenomena are strongly related to bulk crystallinity. The CCD (charge coupled device) is fundamentally MOS type. CCD

14.

OXYGEN FFFEC T O N f I ICTKONIC DEVICF PFKFOKMANCF

623

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Data retention time (sec.)

F I G .4 . Commulative failed bit count\ of data retention time for normal and failed chips (Ohni\hi el al.. IWOb).

-

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Various modes of minuritv c‘arriei injection to DRAM cell node (courte3v of S.

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is an analog device unlike memory or logic. The sensitivity of CCD to

individual defects is one to two orders of magnitude higher than in DRAM (Jastrzebski, 1982). 2 . FAILURE MODESI N LSI D1-vic-i~~

The holding-retention time failure mode is the most serious problem for DRAM devices. The holding time must increase with increasing packing density of DRAM for saving power consumption to refresh the stored information. Figure 4 shows commulative failed bit counts of data retention time for normal and failed chips (Ohnishi et al., 1990b). Several bits with shorter retention time, on the order of 0.1-0.01 sec, are seen in the failed chip and device yield is evaluated only by these failed bits, whereas the retention time of normal chip i s above 1 sec. The holding time failure mode is caused by the diminution of stored charges in a capacitor due to the injection of minority carriers. As shown in Fig. 5 . there are various modes of minority carrier injection to cell

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FIG.6. Leakage current pattern of a processed CCD wafer.

node such as (A) generation current in depletion region, (B) diffusion current from the bulk, (C) forward current from I/O, (D) carriers injected from peripheral circuits and (E) carriers generated by a-particles with high energy. The standby leakage current of SRAM by flipflop circuits must be absolutely reduced because of no periodic refresh operation unlike DRAM. The junction leakage current between the source-drain and substrate is a main cause behind this. For bipolar devices, the emitter-collector (E-C) short circuits crossing base region are a well-known problem, which was first termed pipes by Miller (1960)and are still a matter of concern with decreasing base width. This failure mode is induced by oxide-nitride-edge dislocations and stacking faults formed during LOCOS process (Franz et al., 1981). The pipes are also caused by enhanced diffusion of the emitter dopant atoms along such dislocations (Franz et al., 1981).

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O X Y G E N EFFECT ON ~ I . E , C T R O N I CDEVICE PERFORMANCE

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The CCD image device has a variety of failure modes, such as white spot defects, smear and blooming. Figure 6 shows an example of leakage current patterns, which almost correspond to white spot defect modes, of an entire wafer. The lattice defects corresponding to the swirl are dislocation half-loops (DHLs) distributed at random. These DHLs are considered to be generated by the interaction of field oxide edge stress, suggested by Hu et al. (19761, with microdefects that are caused by the interstitial oxygen distributed in a swirl pattern. 111. Defect Generation

Oxygen atoms that are incorporated in Si during crystal growth and are knocked on by ion implantation, and the residual stress of SiO? film generate crystalline defects. resulting in the device failure modes such as leakage current and oxide film degradation. Furthermore, lattice defects are generated by heavy metal contamination.

I . OXYGEN PRECIPITATE RELATED FAILURE MODES Residual oxygen concentration is closely related to device performance. Figure 7 shows the relationship between residual oxygen concen-

a a

A 10

14

15

16

17

RESIDUAL OXYGEN CONCENTRATION (x10”/cm31

Fic, 7 Holding lime failure rate v 5 iesidudl oxvgen concentrdtion after processing for vdriou\ DRAM devices (Tsuya. 1992)

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H . TSUYA

FIG.8. X-ray topographic picture (upper) and optical cross (lower left) and plane (lower right) pictures of SRAM (Tsuya, 1992).

14.

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OXYGEN EFFECT ON ELECTRONIC DEVICE PERFORMANCE

tration after processing and holding time failure rate obtained for various DRAM devices (Tsuya, 1992). The holding time failure rate increases with increasing residual oxygen concentration, in which oxygen precipitates were hardly observed. On the other hand, holding time failure rate decreases for low residual oxygen concentration. In this region a moderate amount of inner defects due to oxygen precipitation were observed. However, in the case of overprecipitates, holding time failure rate likewise increased, because lattice defects due to oxygen precipitation were generated near the surface region. This situation for SRAM is now discussed. Figure 8 shows an X-ray topographic picture and optical cross and plane pictures of SRAM (Tsuya, 1992). A lot of defects are observed near the wafer periphery compared to the central portion, which shows good denuded Lone from the cross-sectional picture of Fig. 8(a), resulting in good device yield. On the other hand, in the peripheral region, crystalline defects due to oxygen precipitates locate on the device surface region from the plane picture of Fig. 8(b) and increase the leakage current of SRAM. The spatial distribution of residual oxygen concentration meawred by p-FTIR for the previous SRAM wafer is shown in Fig. 9 a ) . The low density of residual oxygen concentration near the periphery is observed. Figure 9(b) shows the uniform distribution obtained from another improved wafer of processed SRAM. The retention failed bit of a Mbit DRAM with a trench cell capacitor was found to be related to oxygen precipitation. The FIB (focused ion beam) marking method was successfully applied to correlate retention failure electrically identified with crystalline defects one by one (Nishio et al.. 1990). Figure 10 shows cross-sectional TEM images of a failing I

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FIG.9. Spatial dihtribution of residual oxygen concentration measured by p-FTIR for the SRAM wafer shown in Fig. 8(a) and for another improved SRAM wafer (courtesy of M. Kit akata) ,

628

n. TSUYA

memory cell, where defects are recognized below the bottom of trench capacitor. EDX analysis and TEM observation showed that these defects were the SiO, amorphouslike octahedral structure that is peculiar to oxygen precipitation (Shimura, Tsuya and Kawamura, 1980a), and this is grown in a high-temperature p-well drive-in diffusion process. From these observations, it was confirmed that oxygen precipitation near the memory cell caused the retention failure of DRAM. This result indicates the importance of optimizing initial oxygen concentration and the necessity of perfect denuded zone (DZ) formation in the active surface layer. Another example of oxygen precipitate defects, which are sometimes called BMDs (bulk micro defects), existing in the N-MOS and C-MOS devices is described (Matsushita, 1989). Figure 11 shows the dislocation density induced at the LOCOS edge as a function of BMD density in N-MOS. Dislocation density increases with increasing BMD density. On the other hand, the dislocation generation relating to the BMD density in C-MOS is quite contrary to that in N-MOS. This is because the C-MOS process includes a well diffusion at a high temperature, which gives rise to oxygen out-diffusion, resulting in the BMD-free zone near the wafer surface. Therefore, BMD distribution must be designed into the device manufacturing process (Matsushita, 1989).

2. RESIDUAL STRESS OF SIO, FILM The residual stress present in thermal SiO, film is relevant to dislocation generation in the Si substrate and induces mechanical damage effects in devices. The mechanical properties of SiO, film depend on growth

FIG.10. Cross-sectional TEM image of the bottom of trench capacitor of failing memory cells (Nishio et al., 1990).

14. OXYGEN EFFFC'I

O N F.LEClRONIC DEVICE PERFORMANCE

629

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Fic, I1 Dislocation density induced N-MOS (MdtsuShita. 1989)

dt

pattern edge as a function of B M D density in

FL. I ? . X-ray topography of bipolar memory device wafers after LOCOS process for (a) and 1000°C (b).

two different growth temperatures of SiO? under 5 atom oxygen pressure at 950°C

temperature (EerNisse, 1979). During growth at 950°C and below, compressive stress is generated in the SiO,. On the other hand, during growth at 975 and IOOO'C, the SiOzfilm gi-ows in a stress-free environment, which is explained by the viscous flow around 965°C (EerNisse and Derbenwick. 1976). In Fig. 12 X-ray topographic pictures of bipolar memory device wafers after LOCOS process for different growth temperatures of SiO, under 5 atom oxygen pressure are shown. In the case of oxidation at 950"C, a high density of defects due to the stress of S O , is generated, as shown

630

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TSUYA

FIG. 13. The concentration profiles of phosphorus, arsenic and recoiled oxygen in Si for 150 keV 10" Pc/cm2 and 315 keV lot6Ast/cm2 through SiO, of 950 A (Hirao et al., 1979).

in Fig. 12(a). However, at the 1000°C oxidation, as shown in Fig. 12(b), defects are drastically reduced due to the release of intrinsic oxide stress. Device failure rate was reduced in accordance with the SiO, growth temperature.

3 . OXYGEN RELATED DEFECTS BY ION IMPLANTATION The ion implantation process induces defects related to oxygen. In practice, ion implantation is carried out through SiO, film in order to avoid the channeling phenomenon and contamination. In this case, however, oxygen atoms are knocked on or recoiled, and oxygen related lattice defects are generated. Figure 13 shows the concentration profiles of P, As and knocked-on oxygen after ion implantation through SiO, of 950 A (Hirao et al., 1979). More oxygen atoms are knocked on by the implantation of larger mass ions. It has been reported that the presence of oxygen atoms can produce an applicable retardation in the growth rate of SPE (solid phase epitaxy) (Kennedy et al., 1977), which is substantially necessary for the annealing process after ion implantation, and also interact with high-dose As atoms during annealing process (Sadana et al., 1983),resulting in lattice defects. From the detailed experiment of lattice defects in high-dose As implantation in a through-oxide layer, it was concluded that the survival or elimination of As-precipitate induced defects was strongly affected by recoiled

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O X Y G E N EFFECI ON t i ECTRONIC DEVICE PERFORMANCE

631

oxygen atoms (Tamura and Horiuchi, 1988). The knocked-on oxygen atoms at about 2 x 10” atonis/cm’ had a strong pinning effect on Asprecipitate induced defects after high-temperature annealing. However, oxygen above 2 x IO”/cm’ had the reverse effect, i.e., dissolution on these defects. The influence of defects induced by recoiled oxygens and unsaturated As atoms on retention failure of DRAM was investigated (Ohnishi et al.. 1990a). Using a method to directly observe the failure bit by TEM, it was found that the leakage of Mbit DRAM was introduced by t h e dislocation line from the sidewall edge across the memory cell, as shown schematically in Fig. 14. The dislocation lines are considered to be generated in connection with the small dislocation loops during the cooling period. From the through-oxide thickness dependence of the dislocation loop density after annealing at 950°C for 30 min and SIMS analysis, it was found that the recoiled oxygens were gettered at the position of the defect generation, and the concentration of the recoiled oxygen had a good correspondence to the defect density. In order to improve the failure of charge leakage in the n +-implanted region, it is important to avoid knocked-on oxygen atoms using the thick through-oxide layer. The failure of n+-substrate leakage was greatly decreased by increasing the through-oxide thickness above SO nm (Ohnishi et al., 1990a). The application of high-energy or high-dose ion implantation for retrograde well formation and a SIMOX (separation by implanted oxygen) substrate has been actively investigated. Especially, SIMOX is a promising substrate for future advanced VLSI. The insulating layer of SIMOX is fabricated by implanting high-dose oxygen atoms with high energy, resulting in defect generation and the surface roughness of the top Si layer. For practical use, it is important to control and suppress crystalline defects generated by implanted oxygen in the device active region. In order Transfer gate LOCOS

I

1

Side wall

I

Disloc\ation Dislocation line

FIG.14. Schematic drawing of the DRAM failed bit (Ohnishi et al.. 1950a).

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H . TSUYA

to reduce defect density, a combination of implantation and subsequent high-temperature annealing procedures has been carried out. Figure 15 shows a cross-sectional TEM image of SIMOX structures formed by high-dose (1.2 x 10'8/cm2 O+/cm2)oxygen implantation at 150 keV after annealing at different temperatures (Yoshino, Kasama and Sakamoto, 1989). Several characteristics layers, marked A , B , C (the buried oxide layer) and D , are observed in the as-implanted stage. In the region A-B, a high density of oxide precipitates, which are identified SO., (0 < x < 2) by XPS, are observed. After annealing at 1280°C for 12 hr, these oxide precipitates disappear by dissolution, and the surface of the top Si and SiO, layers become flat. By a multiple procedure of the implantation of relatively low-dose oxygen and high-temperature annealing, the crystalline quality of SIMOX was dramatically improved (Jaussand et a]., 1985). The evolution of SIMOX defect density is shown in Fig. 16 (Colinge, 1992). It was also reported that the dislocation density decreased to the order of 102/cm2as the dose decreased (Nakashima and Izumi, 1990). Recently, the dislocation-free SIMOX substrate with a dislocation density of less than 7 x 1O-'/cm2 was first reported (Yoshino, 1992). The key process consists of a low-dose single implant (Nakashima and Izumi, 1990) less than 1 x 10'*/cm2and the exclusion of heavy metal contamination during SIMOX

FIG. 15. Cross-sectional TEM images of the SIMOX structure annealed for 5 min at different temperatures: (a) As-implanted, (b) 1 15OoC, (c) 1230°C and (d) 1280°C (Yoshino et al., 1989).

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O X Y G E N EFFFC I O N t I t C T R O N I C DEVICE PERFORMANCE

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breakdown field (MVkm)

FIG 17 Typical dielectric bredkdoun histoprdm of thermally grown SiOZ(Yamabe et rd

. 1983)

formation. The thinner SiO layer fabricated by low-dose ion implantation is more attractive for sub-quarter-micron CMOS devices (Omura et al., 1991).

4. OXIDE FILMDEGRADATION

Much attention has been paid to the quality of thin oxide film, because the thickness of gate oxide film for VLSl is becoming thinner to reduce the propagation delay time. Thermal SiO, film characteristics are greatly influenced by oxygen precipitates near the crystal surface, heavy metal impurities and the surface micro-roughness of a wafer. The dielectric breakdown (DB) histograms of thermal SiOz films are typically separated into three peaks, A , B and C modes as shown in Fig. 17 (Yamabe, Taniguchi and Matsushita, 1983). Among them, B mode failure is closely related to time-dependent dielectric breakdown (TDDB). The experiment of preoxidation high-temperature annealing on the B

634

H . TSUYA

mode failure fraction suggested that surface contamination prior to gate oxidation and microdefects in the Si near the surface were two main origins of B mode defects (Matsushita, 1989; Yamabe et al., 1983). Microdefects are considered to be related to oxygen precipitates from a comparison result of CZ Si with FZ Si wafers, which showed the increase of oxide BD failure with increasing oxygen concentration. However, the oxide BD failure was different from wafer to wafer with the same oxygen concentration, in the range of from about 10I8 to 1.8 X 1018/cm3,suggesting that the contaminated nucleus of the bulk microdefects are related to the B mode (Matsushita, 1989). The influence of heavy metal impurities on gate oxide integrity has been quantitatively clarified (Honda et al., 1987; Hiramoto et al., 1989). Heavy metal impurities are incorporated into oxide film and grown metalsilicides degrade the BD characteristics. Recently, the strong effect of 11-group elements such as Ca, Mg and Zn on dielectric degradation of SiOz films has been discussed (Takiyama et al., 1992). It is also pointed out that atomic scale micro-roughness in the Si wafer surface degrades surface channel mobility (Ohmi, 1991) and the BD characteristics of thin oxide film (Miyashita et al., 1992). The micro-roughness formation is discussed in terms of Si wafer cleaning method (Ohmi, 1990), the nonuniform distribution of the Si vacancy clusters based on the comparison between bulk and epitaxial wafers (Miyashita et al., 1992), oxidation procedures (Carin and Bhattacharyya, 1985) and Si crystal growth condition (Tachimori, Sakon and Kaneko, 1990). The investigation of the BD failure versus growth rate of Si crystals showed that crystals grown at faster pulling rates ( > 1 mm/min) had an increasing BD failure mode, whereas the BD failure mode was much improved for crystals grown at lower pulling rates (